new trends and applications of the casimir effect (casimir) · 2016-09-07 · on long standing...
TRANSCRIPT
1
NEW TRENDS AND APPLICATIONS OF THE CASIMIR EFFECT (CASIMIR)
0. Executive summary of RNP
RNP CASIMIR was a five-year ESF program that was dedicated to research on the Casimir
effect. The aim of the RNP CASIMIR was to foster pan-European collaborations on
established problems and new trends, in Casimir force experiments, applications, and theory
in all subject areas including surface science, materials science, micro/nanotechnologies
through to cosmology and quantum gravity.
The origin of the Casimir effect dates back to the startling realization that was emerged in the
last century that the vacuum, that is, the complete absence of any detectable particles or
energy is far from empty. Theoretically this conclusion originated around 1900 from the work
of Max Planck and the early pioneers of quantum theory. A consequence of the quantum
behavior of electromagnetic fields is that each field mode contains intrinsic ‘zero point’
energy ћω/2 when it is in the lowest energy state. Thus a
field containing no photons - empty space - has a huge
intrinsic energy density. This zero-point energy or
vacuum energy has numerous observable consequences
in atomic or sub-atomic physics. Moreover, two mirrors
facing each other in vacuum are mutually attracted to
each other by the disturbance that they cause of quantum
vacuum fluctuations – a phenomenon first predicted in
1948 by the Dutch theoretical physicist H.B.G. Casimir.
Though the Casimir effect dates back more than 60 years, the field of Casimir physics has
attracted an increasing attention in the last fifteen years, thanks to new experimental
techniques based on recent technological developments in nanotechnology including atomic
force microscopy, and MEMS devices. A number of novel experiments concerning the static
or dynamic Casimir effect have been developed in the last few years in USA and Europe.
New developments have been devoted to observations of the Casimir force in complex
geometries and novel materials (phase-change materials, nanoparticles, carbon nanotubes,
liquids, metamaterials etc.) with a view to applications, especially in nano-machines. Another
focus is on fundamentals such as what the force can tell us about the quantum vacuum, and
for example any possible relationship between zero-point energy and cosmological
observations such as dark energy. In addition sufficiently accurate measurements could reveal
a departure from Newtonian gravity at sub-micron separations providing insight on the new
physics expected to lie beyond the standard model. On the theoretical side, Casimir effect
calculations use numerous different methods ranging from quantum field theoretical
approaches and renormalization methods to quantum statistical methods and scattering
approaches to the wordline formalism.
The RNP CASIMIR united leading scientists from these communities in 11 countries
comprising, at present, 60 research groups (list available on the network website). Though it
started as a relatively small network with 30 groups, the RNP CASIMIR was developed
rapidly almost doubling size in terms of participating research groups, with their work and
interactions leading to more than 300 publications at the end of its term, some of which are
leading papers defining the future trends in the field. Indeed, a number of novel experiments
concerning the static or dynamic Casimir effect have been developed by groups in the
2
network in the last few years. Experimental techniques based on recent technological
developments in nanotechnology including atomic force microscopy, and MEMS devices are
widely employed. On the theoretical side, Casimir force calculations, using numerous
different methods ranging from quantum field theoretical approaches and renormalization
methods to quantum statistical methods and scattering approaches to the world-line
formalism, have been developed. These research efforts have been strongly supported by
short visits and exchange grants 70 in total for the period 2008-2013.
In fact the RNP CASIMIR has provided a dynamic forum for a quick and efficient exchange
of techniques and ideas as well as the close collaboration between experiment and theory by:
Integrating and disseminating the work carried out by the Casimir physics communities in different
countries in Europe by the exchange of junior researchers and students between research groups
via short visit or exchange grants
Facilitating the smooth exchange of new ideas
Providing interdisciplinary training and foster collaboration by creating links with leading groups
in different areas of adjacent communities
Providing transmission of new concepts and techniques from research frontiers to the basic
training level by organising conferences, topical workshops, and schools
Support was given to various science meetings (conferences, workshop, schools) where the
CASIMIR presence was an important part of the event’s profile. In addition, the CASIMIR
program was also part of several activities within EU and national programs, as well as
international collaborations with the USA, Mexico, Brazil, Hong-Kong/China, and Argentina.
All these actions were necessary to maintain the theoretical and experimental activity at a
highly competitive level. The expected benefits from the CASIMIR programme are a
consolidation and increase of the European Casimir physics community and an enhanced
visibility and attractiveness of European Casimir physics for scientists and especially students
and younger people all over the world.
1. RNP objectives
The objective of the RNP CASIMIR was to foster European and pan-European collaborations
on long standing problems in the field as well as on new trends in Casimir force experiments,
applications, and theory. Although the Casimir effect dates back more than 60 years, the field
of Casimir physics has attracted an increasing attention in the last fifteen years, thanks to new
experimental techniques based on recent technological developments in nanotechnology
including atomic force microscopy, and MEMS devices. Indeed, since the pioneering
experiments in 1997 by Lamoreaux, the Casimir force has regained a lot of interest and it was
remeasured already several times with greatly improved precision. As a result the field
received significant attention, and continuous to grow, for micro/nano-technology
applications and fundamental physics.
The core research topics within the CASIMIR network, studied by both experimentalists and
theorists, were streamed in the following interrelated areas:
Casimir effect: measurement and theory Casimir force in complex geometries and
novel topologies: control of Casimir force
& applications to NEMS; patterned or
corrugated surfaces, nanospheres, small
spheroïd shaped bodies, edge effects,
vacuum torques, beyond proximity force
approximation (PFA) measurements and
calculations.
New materials and their optical properties:
control of Casimir force & applications to
MEMS/NEMS; Carbon nanotubes,
3
nanoparticles, metamaterials, quasicrystals,
superconductors, photonic crystals, phase
change materials (avoid parentheses)
Repulsive and lateral Casimir forces
Thermal Casimir effects
Applications in nanophysics, biophysics,
and disordered systems
Challenges in vacuum properties Casimir effect, vacuum energy, gravity and
cosmology: Yukawa and Chameleon
interactions
Casimir effect and tests of the equivalence
principle
Dynamical Casimir effect: Unruh effect,
vacuum friction and decoherence
Related Casimir topics Critical Casimir Forces
Dispersion forces in liquids
Casimir Polder interaction with BEC and
molecules
Quantum friction and Casimir momentum
Based on the core research topics, a number of novel experiments concerning the static or
dynamic Casimir effect have been developed by groups in the network in the last few years.
Experimental techniques based on recent technological developments in nanotechnology
including atomic force microscopy (AFM), and MEMS devices are widely employed. On the
theoretical side, Casimir force calculations, using numerous different methods ranging from
quantum field theoretical approaches and renormalization methods to quantum statistical
methods and scattering approaches to the world-line formalism, have been developed. These
research efforts have been strongly supported by short visits (56 in total for the period 2008-
2013) and exchange grants (14 in total for the same period). Support was given to various
science meetings (14 conferences, workshops or schools) where the CASIMIR presence was
an important part of the event's profile. In addition, the CASIMIR program was also part of
several activities within EU and national programs, as well as international collaborations
with the USA, Mexico, Brazil, Hong-Kong/China, and Argentina. All these actions were
necessary to maintain the theoretical and experimental activity at a highly competitive level.
Some indicative research highlights: For a more detailed overview see appendix 7.7
With up-to-date techniques derived from Scanning ProbeMicroscopy the Casimir force can be precisely measured, but its absolute measurement together with themirror's distance hidesmany
instrumental difficulties.
A vacuum may be devoid of matter, but its shape is still important. The strength of the Casimir force caused by quantum fluctuations in the space
between surfaces is critically dependent on their nanometre-scale shape
Correlation geometry - temperature –dissipation: Force between metallic plane and sphere at room temperature: Plasma and Drude always closer than expected from PFA - Ratio at large L never approaches the factor 2 given by PFA
4
2. RNP activities: scientific quality and impact
Main conferences, schools, workshops
In order to maintain control of current research activity within the Programme we have
planned and supported the following conferences /schools / workshops: 2008, November, France “Network Meeting 2008”
2009, August, USA “Casimir force and their measurements”
2009, September, USA “Quantum Field Theory under the Influnce of External Conditions
(QFEXT09)”
2009, September, USA “New Frontiers in Casimir Force Control”
2010, April, France “Casimir, van der Waals and nanoscale interactions”
2010, May-June, France, “Precision Physics of Simple Atomic Systems”
2010, November, Spain, "Fluctuations and Casimir Forces".
2011, January, Norway “Observability and theoretical grounding of thermal Casimir forces”
2011, May, Austria “Casimir forces: effects of clusters and molecules close to and on surfaces.”
2011, June, Italy “Dynamical Casimir effect”
2011, September, Spain “Quantum Field Theory under the Influence of External Conditions
(QFEXT11)”
2012, March, The Netherlands “Casimir physics School-workshop”
2012, July, The Netherlands, “Kelvin Probe Force Microscopy analysis of surface potentials and
patch effects in Casimir force measurements”
Tallor Casimir forces by employing materials whose optical properties can be changed in response to a simple stimulus.
:Casimir effect put to work as a nano-switch (July 2010)
The Casimir force is higher for crystalline than amorphous Phase changing materials (PCMs). The contribution of free electrons (Drude term) and the change of bonding to the Casimir force contrast suggest potential pathways to optimize force contrast for MEMS applications (Adv. Funct.
Mat. 22, 3729, 2012)
►►SSiimmuullaattee aa mmiirrrroorr mmoottiioonn bbyy cchhaannggiinngg
mmiirrrroorr rreefflleeccttiivviittyy
►►TThhee sseemmiiccoonndduuccttoorr rreefflleeccttiivviittyy iiss ddrriivveenn
bbyy llaasseerr iirrrraaddiiaattiioonn mmiirrrroorr sswwiittcchheess
ffrroomm ccoommpplleetteellyy ttrraannssppaarreenntt ttoo
ccoommpplleetteellyy rreefflleeccttiivvee ((ffoorr mmiiccrroowwaavveess))
Dynamical Casimir effect: Padova experiment
Probing the vacuum…!
Electrostatics of surfaces: Varying surface voltages, known simply as patch potentials (in real metal surfaces are typically composed of randomly oriented crystallites), thereby giving rise to a nonuniform potential over the metal’s surface. Patch potentials have important implications in gravitational measurements on elementary charged particles, tests of the general theory of relativity, ion trapping, and the physics of Rydberg atoms . Because electrostatic patch potentials give rise to forces between neutral conductors in the micrometer range must be accounted for in the analysis of Casimir force experiments.
Direct comparison of the residual pressure δPDrude between the experimental pressure and the Drude prediction with patch pressure Ppatch ; Phys. Rev. A 85, 012504 (2012)
Quasilocal model
5
2012, October, Argentina, “PASI Casimir School”
Total events: 14
Exchange grants, short visits, awards The program has pointed out the necessity to facilitate exchanges between members of the
network and collaborating parties. We have supported the exchange of ideas and stimulated
new collaboration during schools/workshops which enabled multi-partner interactions as well
as proposals for short visits and exchange grants between two partners. For this purpose we
reserved a certain budget to provide a certain amount of financial support for these type of
activities (Appendices 3 and 4). ●Short visit grants: 4 in 2008, 12 in 2009, 12 in 2010, 20 in 2011, 6 in 2012, 2 in 2013-Total: 56
●Exchange grants: 1 in 2008, 4 in 2009, 2 in 2010, 3 in 2011, 3 in 2012, 1 in 2013-Total: 14
●Junior Paper Award: "CASIMIR-QFEXT Junior Paper Award 2009" (Sponsored by the CASIMIR
network) is given to Dr. J. Munday (Caltech USA) and Dr. S. Ellingsen (Norwegian University of
Science and Technology in Trondheim); "CASIMIR-QFEXT Junior Paper Award 2011" (Sponsored
by the CASIMIR network) is given to A. Canaguier-Durand.
Publication activities
Website of the network: http://www.casimir-network.com/
Published research papers: There are more than 300 research papers (2008-2013) published in
high ranking research journals in physics and technology (see Appendix 7.8).
Editorial activities
These activities an important issue in the network research dissemination and establishing
future leadership in the field. Among the results of these activities we mention the following
highlights:
Nature News and Views - Shaping the void: (A. Lambrecht, Nature 454, 836 (2008)).
Book publication - Advances in the Casimir Effect: M. Bordag, G. L. Klimchitskaya, U. Mohideen,
and V. M. Mostepanenko (Oxford U. Press, New York, 2009) The Casimir Effect and Cosmology: A volume in honor of Professor Iver H. Brevik (member of our
CASIMIR network). This special volume represents the collection of articles devoted mainly to
Casimir effect and Cosmology.
Casimir Effect, Zeta Functions, and Cosmology by Emilio Elizalde, Consejo Superior de
Investigaciones Cinetificas, Universitat Autonoma de Barcelona, Fac. CienciesICE/CSISC and IECC
Bellaterra (Barcelona), Spain.
Europhysics News: March-April 2009, p.13, “Non-contact Casimir force measurements”
(www.europhysicsnews.org/articles/epn/pdf/2009/02/Whole_issue.pdf)
NEW SCIENTIST/TECH July 2, 2010: “Casimir effect put to work as a nano-switch”
Lecture Notes in Physics: Five members of the CASIMIR network contributed chapters (review
articles) for a book in Springer-Verlag series 'Lecture Notes in Physics'. Edited by D. Dalvit, P.
Milonni, D. Roberts, F. da Rosa (Los Alamos National Lab, USA).
Editor EuroPhysics Letters: A. Lambrecht is serving as co-editor of the leading European journal in
physics the EuroPhysics Letters (EPL)
Collaboration/interaction with other programs & Industry
The importance of the Casimir field, in both fundamental physics and blue-sky technology
was recognised initially in Europe and has attracted funding from the European Commission
(NANOCASE project) and latter by the present CASIMIR network. Furthermore, the
CASIMIR program interacts with a variety of related research programs:
Short visits (SV) grants + Exchange (E) grants: 70
Publications where RNP is explicitly referenced: 111 ~1-2 Publications / grant
6
ESF EuroQuasar program MIME (Prof. M. Arndt, Austria)
http://www.esf.org/activities/eurocores/running-programmes/euroquasar.html
Collaboration France-Brasil CAPES-COFECUB program "Casimir effect and applications"
(Coordinator A. Lambrecht)
FP6 STREP NANOCASE http://www.nanocase.le.ac.uk since 2006 (Prof. C. Binns)
Label CARNOT with LETI/CEA at Grenoble «Nanostructures for MEMS in IC» since 2007 (Dr. A.
Lambrecht)
ANR Pnano “Modelling and application of nanophenomena at nanoscales influencing NEMS” since
2007 (A. Lambrecht)
Joint organization of research workshop "Fluctuations and Casimir Forces" between CASIMIR
network and ESF activity 'Exploring the Physics of Small Devices', Nov. 4-6, 2010, Hotel Villalba,
Tenerife, Spain.
The PhD thesis: P.J. van Zwol, Contact mode Casimir and capillary force measurements, was partly
funded by TNO Industrial Research Labs (The Netherlands)
Member of the network (G. Palasantzas) participates in a ESA project related to Optical/van der
Waals bonding of stiff materials for space self-assembly exploration.
PhD Theses from RNP research groups 2008-2013
A. Canaguier-Durand, Multipolar scattering expansion for the Casimir effect in the sphere-plane
geometry (Thesis advisor A. Lambrecht / Graduated September 2011)
G. Messineo, Dynamic Casimir Experiment (Thesis advisor G. Carugno/Graduated 2011)
S. A. Ellingsen, Dispersion forces in Micromechanics (Thesis advisor I. Brevik/Graduated 2011)
P.J. van Zwol, Contact mode Casimir and capillary force measurements (Thesis advisor
G.Palasantzas /Graduated 2011)
S. P.J. de Man, Multi-lockin instrument for surface force measurements and applications to
Casimir force experiments (Thesis advisor D. Iannuzzi / Graduated 2011)
R. Messina, Casimir - Polder force between atom and surface : geometrical and dynamical effects
(Thesis co-advisors A. Lambrecht and R. Passante / Graduated 2010)
S. Kawka, Moment de Casimir : Effet du Vide Quantique sur l’Impulsion d’un Milieu Bi-
anisotrope (Thesis advisor B.A. van Tiggelen / Graduated 2010)
J. Lussange, The Casimir energy and radiative heat transfer between nanostructured surfaces,
(Thesis advisor A. Lambrecht/Graduated September 2012)
3. European added value and RNP visibility
The opportunities provided by the CASIMIR program up to now played an essential role in
the emergence of the EU Casimir community as a dominant world leader in Casimir physics.
The high quality of the papers published up to now provide a clear proof of the European
added value of the CASIMIR program in the global Casimir physics community. Because of
intense research by renowned groups within the program, the CASIMIR network has become
the dominant reference in the field coordinating a major part of the international research
activity on this increasingly important subject. Moreover, there is close interaction with main
groups in USA and we have supported their conferences/workshops financially and with
direct scientific participation. Therefore, the ESF network CASIMIR aimed to excel via a
strong international collaboration.
In particular the following activities have been supported in the USA/Americas:
2009, August, Yale University, USA “Casimir force and their measurements”
2009, September, Oklahoma, USA “Quantum Field Theory under the Influence of External
Conditions (QFEXT09)”
2009, September, Santa Fe, USA “New Frontiers in Casimir Force Control”
2012, Casimir PASI School organized by USA-Argentinean researchers (including also members
of our network - Prof. R. Esquivel-Sirvent/Mexico) Oct. 2012 in Argentina.
7
We organized extra topical strategic meetings, where researchers from outside the network
were also invited if a close relation with the network activities existed. These meetings were:
2011, January, Norway “Observability and theoretical grounding of thermal Casimir forces”
2011, May, Austria “Casimir forces: effects of clusters and molecules close to and on surfaces.”
2011, June, Italy “Dynamical Casimir effect”
2012, July, The Netherlands, “Kelvin Probe Force Microscopy analysis of surface potentials and
patch effects in Casimir force measurements”
4. RNP management and finances
Financial expenditures are reported in the Appendices 5 and 7-9. As stated above, we
allocated a significant part of the budget towards short term visits (up to 15 days;
reimbursed on a per diem basis of 85 EUR plus actual travel expenses up to a maximum of
500 EUR), exchange grants (duration from 15 days up to 6 months; reimbursed on the
basis of an allowance of 1,600 EUR per month / 400 EUR per week / 57 EUR per day plus
actual costs for travel, up to a maximum of 500 EUR), and science meetings each year,
including support of smaller topical strategic workshops.
The administrative structure of the CASIMIR network has operated without difficulty: the
steering committee met once (or twice if necessary) per year in some convenient place
where the budget for the whole year is approved during the first meeting. All other
business was conducted via e-mail.
All decisions on budget are reported in the minutes of the steering committee meetings.
Short grant applications are managed by the executive committee (G. Palasantzas, S.
Reynaud, and M. Bordag), while longer grants and science meetings applications are
managed by the steering committee. Some applications have been declined due to wrong
area of expertise and lack of scientific visibility.
There have been changes in the membership of the steering committee (G. Palasantzas
replaced D. Iannuzzi since Jan. 2010, S. Reynaud replaced A. Lambrecht since Oct. 2010,
G. Palasantzas replaced A. Lambrecht as chairman Nov. 2010). The number of
participating groups, 60 at present, has been doubled since the start of the network in 2008.
5. Publicity and publications: scientific quality and impact
Public and scientific outreach The CASIMIR network maintained its own website (http://www.casimir-network.com/) which has
been proven to be successful in: attracting applications for support, disseminating scientific
information, advertising job openings within member institutions, announcing conferences or
workshops within the scope of the program (including link at the corresponding websites), and
providing list of member groups associated with research on Casimir physics
We produced a brochure of the CASIMIR network with the help of ESF in 2008-2009
The CASIMIR network was advertised in the European Physical Society (EPS) news website:
http://www.eps.org/news/newsfeed2/
Exceptional conference of EPS (Conférence exceptionnelle de l'EPS) on Casimir effect, presented
by S. Reynaud and A. Lambrecht at the Headquarters of EPS in Mulhouse, March 18, 2010
(attended by EPS people, staff and students from the University and High schools in Mulhouse).
Public dissemination activities in UK:
School Talk, Denbigh School Milton Keynes, Nanotechnology, 19/05/08, 50 school students year
8 – 10 students year 14 – 16, Projects: NANOSPIN, NANOCASE, ESF Casimir network
Talk at Sherwood Observatory, What Lies Beneath the Void, 30/09/08, 50 adults, Projects:
CasFoCot, ESF Casimir network
Lecture to A level students at Leicester Physics Masterclass. Nanotechnology, 1/04/09, 12
students 11-years-old, Projects: CasFoCot, ESF Casimir network
8
School Talk, Cherwell school, Oxford, Nanotechnology, 11/11/09, 30 students 12-years old,
Projects: CasFoCot, ESF Casimir network
The current network chairman(G. Palasantzas) represented the CASIMIR network at the ESF
meeting April 11-12 (2011) in Dubrovnik (Croatia).
Scientific publications enabled by the RNP members (more than 300): Appendix 7.8
As it is outlined briefly above and confirmed also by the number and high quality of scientific
publications (Appendix 7.8), there has been strong progress regarding the objectives (section
1) of the CASIMIR network, which continue to represent the main drive of the activities in
this field. Moreover, the CASIMIR network has led to consolidation and increase of the
European Casimir physics community and an enhanced visibility and attractiveness of
European Casimir physics for scientists and students all over the world. Nevertheless, still lots
of work remains to be done in order to confront long standing problems in fundamental
physics and towards new material systems allowing control of the magnitude and sign of the
Casimir force for nanotechnology applications.
6. Future perspectives
The Casimir effect has seen a very rapid development in recent years, due to its importance
for fundamental physics and technological applications. It has large overlaps with other
important areas of physics, such as condensed matter (material properties), nanophysics (key
role for micro- and nanodevices), and statistical physics (surface roughness and disorder). It
also has connections with gravitation (search for new forces beyond the standard model),
astrophysics and cosmology, chemistry and biology. The fast dissemination of the latest
results, the smooth exchange of new ideas and the interdisciplinary training and collaboration
are necessary to uphold the current trend in theoretical investigations and experimental
engagement on a competitive level.
Casimir physics and fluctuation induced forces find applications in various domains of
physics and related disciplines. Indeed the precise laws governing the long-range interactions
between atoms, molecules, clusters, bio-assemblies or surfaces amongst each other, immersed
in vacuum, in air or in a liquid are important not only for physics but also for biological and
chemical processes. Understanding the Casimir force in a whole variety of flexibly shaped
boundaries will open novel techniques in the engineering of nano-mechanical systems.
Understanding Casimir phenomena of sticking and adhesion phenomena may revolutionize
the engineering possibilities of micro and nanomachines. The expected scientific benefits
would be in the future:
Evaluation of fluctuation induced phenomena on different scales (cosmological, mesoscopic,
nanometric) and under different conditions (vacuum or medium assisted)
Precise understanding of dynamical Casimir and Casimir-like effects including a non controversial
quantum description of moving bodies
Development and use of applications of Casimir and Casimir-like phenomena in nanomechanical
devices (NEMS, opto-mechanical, atom chips…)
Evaluation of the role and utilization of dispersion forces in atomic and molecular physics (in
particular in matter wave interferometry)
Assessment of the role of van der Waals forces in proteins, DNA and macromolecules and other
bio-assemblies (with possible medical applications)
Understanding the role of Quantum Vacuum in fundamental physics (including the search for new
forces beyond the Standard model and relations to Dark Matter/Energy)
Focus of Casimir forces applications to industry (stiction, alignment issues lithograpghy
components, robotics, friction, superadhesion, macroscopic assembly in space etc..)
9
Appendix 7.1: Program steering committee Prof. Astrid Lambrecht (Chair 04/08-11/10)
Laboratoire Kastler Brossel
Université Pierre et Marie Curie, CNRS, ENS
Paris, France
Tel: +33 1 44 27 51 53
Fax: + 33 1 44 27 38 45
Email: [email protected]
Prof. Serge Reynaud (10/10-)
Laboratoire Kastler Brossel
Université Pierre et Marie Curie, CNRS, ENS
Paris, France
Tel : +331 44 27 37 50
Fax: + 33 1 44 27 38 45
Email: [email protected]
Professor Markus Arndt
Institute of Experimental Physics
University of Vienna
Vienna, Austria
Tel: +43 (0)1 4277 51205
Fax: +43 (0)1 4277 9512
Email: [email protected]
Professor Chris Binns
Department of Physics and Astronomy
University of Leicester
Leicester LE1 7RH, UK
Tel: +44 116 2523585
Fax: +44 116 2522770
Email: [email protected]
Dr. Michael Bordag
Institut für Theoretische Physik
Universität Leipzig
Leipzig, Germany
Tel: +49 341 97 32427
Fax: +49 341 97 32548
Email: [email protected]
Professor Iver Brevik
Department of Energy and Process Engineering
Norwegian University of Science and Technology
(NTNU)
Trondheim, Norway
Tel: +47 735 93555
Fax: +47 735 93491
Email: [email protected]
Professor Markus Büttiker
Department of Theoretical Physics
Université de Geneve
Genève, Switzerland
Tel: +41 022 379 68 60
Fax: +41 022 379 68 70
Email: [email protected]
Dr. Giovanni Carugno
Istituto Nazionale di Fisica Nucleare
Padova, Italy
Tel: +39 (0)49 8068 421-429
Fax: +39 (0)49 872 6233
Email: [email protected]
Professor Emilio Elizalde
Consejo Superior de Investigaciones Cientificas
Universitat Autonoma de Barcelona
Barcelona, Spain
Tel: +34 93 581 4355
Fax: +34 93 581 4363
Email: [email protected]
Professor Raul Esquivel-Sirvent
Instituto de Fisica
Universidad Nacional Autonoma de Mexico
Mexico, Mexico
Tel: +1 525 5622 6063
Email: [email protected]
Prof. Davide Iannuzzi (04/08-12/09)
Faculty of Science
VU University Amsterdam
Amsterdam, The Netherlands
Tel: +31 20 598 7577
Fax: +31 20 598 7992
Email: [email protected]
Dr. Ariel Ricardo Guerreiro
Departamento de Física
Universidade do Porto
Porto, Portugal
Tel: +351 226 082 611
Fax: +351 226 082 679
Email: [email protected]
Dr. George Palasantzas (01/10-, Chair 11/10-)
Zernike Institute for Advanced Materials and
Materials innovation institute M2i
University of Groningen,
Groningen, The Netherlands
Tel: +31 50 363 4272
Fax: +31 50-363 4879
Email: [email protected]
ESF Liaison
Dr. Jean-Claude Worms
Head of Science Support OfficeScience
Ms. Catherine Werner
Administration
Physical and Engineering Sciences Unit (PESC)
European Science Foundation
1 quai Lezay-Marnésia
BP 90015
67080 Strasbourg cedex
France
Tel: +33 (0)3 88 76 71 28
Fax: +33 (0)3 88 37 05 32
Email: [email protected]
10
Appendix 7.2: Contributing organizations
Austria: Fonds zur Förderung der wissenschaftlichen Forschung in Österreich
(FWF), Austrian Science Fund
France: Centre National de la Recherche Scientifique (CNRS), National
Scientific Research Centre
Germany: Deutsche Firschungsgemeinschaft (DFG), German Science
Foundation,
Italy: Istituto Nazionale di Fisica Nucleare (INFN), National Institute of Nuclear
Physics
Mexico: Red de Grupos de Investigación en Nanociencia y Nanotecnología
(REGINA-UNAM), Group of Investigation in Naniscience and Nanotechnology
Norway: Forskningsradet, Research Council of Norway
Portugal: Fundação para e Ciência e a Tecnologia (FCT), Science and
Technology Foundation
Spain: Consejo Superior de Investigaciones Cientificas (CSIC), National Higher
Council for Scientific Research, and Ministerio de Educación y Ciencia (MEC),
Ministry of Science and Education
Switzerland: Schweizerischer Nationalfonds (SNF), Swiss National Science
Foundation,
The Netherlands: Nederlands Organisatie voor Wetenschappelijk Onderzoek
(NWO), Dutch Organisation for Scientific Investigations
United Kingdom: Engineering and Physical Sciences Research Council (EPSRC)
11
Appendix 7.3: List of science meetings 2008 - 2013
In 2008
CASIMIR Network Meeting: The meeting took place at November 29-30, 2008 at the Abbey
of Royaumont, France. After the introduction the actual scientific part of the meeting started.
The talks were gathered by country, where each networking group gave a single talk
presenting the ensemble of their activities related to research in the Casimir effect. All
together there were 26 talks from 11 different countries. A broad spectrum of different
scientific aspects was covered:
• Thermal Casimir effects (in and out of thermal equilibrium)
• Casimir force in complex geometries and novel topologies with view on control of Casimir
force & applications to NEMS (patterned or corrugated surfaces, nanospheres or small spheroïd
shaped bodies, edge effects, vacuum torque acting on anisotropic or structured bodies, beyond PFA
measurements and calculations, repulsive & lateral Casimir forces) • New materials and their optical properties with view on control of Casimir force &
applications to NEMS (Carbon nanotubes, nanoparticles, metamaterials, quasicrystals,
superconductors, photonic crystals, repulsive & lateral Casimir forces) • Applications in nanophysics, biophysics
• Dynamical Casimir effect, Unruh effect, vacuum friction and decoherence
• Casimir effect, vacuum energy, gravity and cosmology
• Casimir and Yukawa type forces
• Van der Waals forces and dispersion forces in liquids
• Casimir Polder interaction with BEC and molecules
In 2009
2483 - Casimir forces and their measurements (Casimir 2009): This workshop has been
organized as an integrated satellite workshop to the 12th International Conference on
Noncontact Atomic Force Microscopy (NC‐AFM) which was held at Yale University
(USA) August 11-12. The two‐day Casimir 2009 workshop received 24 contributed talks
and 2 invited talks with a total of 86 (day 1) and 122 (day 2) participants. The meeting
attracted theorists and experimenters in the Casimir community, giving them a great
opportunity to expand their knowledge in experimental techniques and detailed
procedures in atomic force microscopy.
2511 - Quantum Field Theory Under the Influence of External Conditions (QFEXT09):
The Conference was held at the University of Oklahoma, Norman, USA during the period
21–25 September 2009. This conference celebrated the Centenary of the birth of H. B. G.
Casimir (1909–2000). Approximately 108 scientists from more than 25 nations and four
continents were participants. 78 talks were given, of which 27 were plenary or invited, and
there were 10 posters presented.
2398 - New Frontiers in Casimir Force Control: The workshop took place in Santa Fe,
New Mexico (USA), from September 27 to September 29, 2009, at the hotel Inn of
Loretto, a premier hotel in the heart of the historic plaza of Santa Fe. The workshop
brought together a total of 88 participants from all over the world, with a substantial
number from Europe, including especially junior researchers. There were 20 talks by
leaders in the field of Casimir physics, plus a keynote talk at the conference banquet by
Prof. Igor Dzyaloshinkii (UC Irvine), one of the fathers of the field.
12
In 2010
2923 - Casimir, van der Waals and nanoscale interactions: The workshop Casimir, van
der Waals and nanoscale interactions was held in L’Ecole de Physique des Houches in
France from Sunday 11 April to Friday 16 April. It was organized to provide its
participants an overview of the state-of-the-art in the field of the Casimir effect and of
some of the related research areas. The workshop brought together a total of 67
participants from all over the world, with a substantial number from Europe, including
especially junior researchers. There were given 16 one hour talks and 19 shorter of 25
minutes talks from young researchers. The school covered several topics (Casimir effect,
Van der Waals interactions, Tests of fundamental interactions, Critical Casimir effect,
Nano-optics and nano-photonics, Mesoscopic physics, Instrumentation)
2964 - Precision Physics of Simple Atomic Systems: This is one of a series of
international conferences gathering since 2000 every other year 50 to 100 physicists in
different places. The 2010 edition took place in Les Houches, in France, from May 30 to
June 4. The conference is devoted to precision studies of simple atomic and molecular
systems in order to see something beyond atomic physics. That involves various issues
from particle and nuclear physics, atomic and molecular physics, astrophysics, metrology,
etc. In particular, we consider tests of various fundamental theories and constraints on
effects of new physics beyond standard model, which naturally include searches of the 5th
force.
In 2011
3522 - Observability and theoretical grounding of thermal Casimir forces: Thermal issues
in connection with the Casimir effect have been under study for actually several years, and
this meeting contributed to further understanding of the effect. This was a topical meeting
organized by Prof. I. Brevik for two days in 26- 27 January 2011 (with 9 participants) at
the Department of Energy and Process Engineering together with the Institute of Physics
of the Norwegian University of Science and Technology (NTNU). They were invited two
external from the network people having worked in this specific area.
3509 - Casimir forces: effects of clusters and molecules close to and on surfaces: 2.5 day
workshop with 17 participants 5-7 May 2011. In this topical workshop theory and
experiment shall work together to tackle two very well-focused questions: 1. How do
Casimir forces influence molecular beams close to real-world materials in real-world
nanofabricated geometries? 2. How can Casimir forces between two surfaces be modified
by the deposition of size-selected nanoclusters of various types and shapes?
3427 – Dynamical Casimir effect: This is a 3 day workshop with 30 participants organized
with the support of the European Casimir Network at the National Institute in
Padova/Venice in June 5-8, 2011. For the last 10 years, the interest to various dissipative
effects in quantum vacuum, especially to the creation of quanta due to the motion of
boundaries or changes of their properties, has increased significantly, both from the
theoretical and experimental points of view. The workshop will gather most of the people
that are deeply involved in such physics, opening a discussion between theorists and
experimentalists to evaluate the actual status of the research in this field and to look
together for possible solutions of the emerging problems.
13
3635 - Tenth conference on QUANTUM FIELD THEORY UNDER
THE INFLUENCE OF EXTERNALCONDITIONS (QFEXT11)
(http://benasque.org/2011qfext/): QFEXT11 from Sept. 18-24 held in
Benasque (Spain), with 106 participants was a continuation of a series
of workshops of the same title held at the University of Leipzig in
1989, 1992, 1995, 1998, 2001, 2007, at the University of Oklahoma in
2003 and 2009, and at the University of Barcelona in 2005. Started
with the intention of bringing about an East-West scientific dialog,
QFEXT developed into one of the most prominent meetings in the field of the Casimir
effect, vacuum energy, and related questions in several areas, ranging from quantum field
theory and cosmology to atomic, subnuclear, and experimental physics. Typically
mathematical questions related to spectral geometry are represented as well. These
meetings have created a unique atmosphere where theoreticians, mathematicians and
experimentalists are brought together for a week, where talks by colleagues that they
might rarely hear otherwise often spark lively debate and result in numerous
collaborations. QFEXT11 will also celebrate the 75th anniversary of the seminal paper
'Consequences of the Dirac Theory of the Positron', by W. Heisenberg and H. Euler
(Zeitschr. Phys. 98, 714-732, 1936), which played an important part in establishing the
study of quantum fields in classical background fields. It is planed to include a special
session devoted to Heisenberg-Euler effective Lagrangians and their impact in modern
physics.
In 2012 4045 - Casimir School-Workshop 2012 (March 5-16, 2012) : It was organized at the
Lorentz Center of Leiden University (The Netherlands) with 69 participants. The
combined school-workshop aimed to explore developments on a global scale in the
Casimir field as an education and research forum in Casimir physics. The school covered
the basics in depth, general formalism, experiments and moving into the more advanced
technical aspects, with a clear overview of the state of the art
in the field. For this purpose we gave able time for young
researchers and advanced researchers to interact in class and
get acquainted with each other and initiate interactions and
further collaborations (starting from the school and further
focused by the workshop. Subsequently, therefore, the school
will be followed by a workshop with the aim to further
connect people doing current advanced work in the field of
surface force measurements and micro/nano technologies
with those who work on current problems of quantum field
theory derived forces and to expand their understanding of
these forces in common problems from nicro/nano
technologies to gravity and laboratory cosmology :
Casimir school : Based partly on the CASIMIR network program, the list of topics for the
school were grouped into the following three major topics : i) Casimir effect :
measurement and theory, ii) Challenges in vacuum properties, iii) Casimir interfaces
Casimir workshop : The workshop focused on current advanced Casimir research and
common topics : Progress in Casimir forces for complex geometries - novel topologies,
Measurements and calculations of Casimir forces for new materials – MEMS/NEMS,
Electrostatics in force measurement : patch effects and contact potentials, Lateral and
repulsive Casimir forces-MEMS/NEMS, Measurements and manifestations of the thermal
14
Casimir forces, Casimir-Polder interactions and thermal effects, Vacuum energy in
quantum field theory and cosmology.
The school-workshop was open to participation by the Dutch and international research
community via registration at the website of the school-workshop.
4231 – Workshop "Kelvin Probe Force Microscopy analysis of surface potentials and
patch effects in Casimir force measurements" at the University of Groningen, The
Netherlands, 28 - 29 June 2012 with 12 participants. The importance of measuring the
electrostatic force is widely recognized in the Casimir community. It is now timely to
organize a dedicated workshop to discuss this interface which is so important in the
comparison with theory of the thermal Casimir force. The workshop will gather
specialists coming from different domains, with the aim of exchanging information on the
problems of interest at this interface as well as means of solving these problems. With
Kelvin Probe force Microscopy (KPFM), the work function of surfaces can be
characterized at nanoscales. The work function relates to many surface phenomena,
including reconstruction of surfaces, doping and band-bending of semiconductors, charge
trapping in dielectrics etc.. The map of the work function produced by KPFM gives
information about the composition and electronic state of the local structures on the
surface of a solid. It allows one addressing the challenge of patch characterization of real
surfaces which also show roughness.
4042-PASI School/Workshop on "Frontiers in Casimir Physics" 8-19 October 2012,
Ushuaia, Argentina with 67 participants. The science of fluctuation-induced interactions,
also generally known as Casimir interactions, is a fast evolving interdisciplinary field of
research worldwide, ranging from quantum physics, condensed-matter, and
nanotechnology, all the way to chemistry and biology. This PASI will bring together a
team of top researchers and lecturers, postdocs, and advanced graduate students to engage
in state-of-the-art training and discussions. This school and workshop will provide a
unique environment for a productive interdisciplinary exchange of ideas among lecturers
and participants. The latest advances and innovations in analytical techniques, numerical
algorithms, and experimental measurement techniques will be discussed. Topics of the
school will include Casimir theory and experiments, quantum friction, quantum
plasmonics, and atom-surface Casimir interactions.
15
Appendix 7.4: List of short visits and exchange grants
Short visit grants 2008-2013
16
17
18
19
20
21
22
Exchange grants 2008-2013
23
Appendix 7.5 & 7.6: Expenditure of funds by major headings 2008-2013
Conference, schools and workshops: 236322 €
Exchange grants: 57049 €
Short visits: 33677 €
Steering committee meetings: 35183.32 €
ESF administrative costs 53200 €
Publications and publicity: 9877.59 €
24
Appendix 7.7: Detailed assessment of results achieved 1. Material properties, liquids, surfaces The interaction between surfaces of real materials is actively studied by members of the
network due to its relevance in technology applications involving the Casimir force. Indeed,
the magnitude of the Casimir force between real materials is modified by the dielectric
function [1] and morphology of the interacting surfaces and the dielectric function of the
intervening medium offering the possibility to control the magnitude and sign of the force. A
promising avenue to control the Casimir force is to use novel materials, such as Carbon
nanotubes, nanoparticles, metamaterials, quasicrystals, birefringent materials,
superconductors, photonic crystals, liquids, and switchable materials. These materials show
unique and controllable optical properties and they could be used to control the Casimir force
in a predictable manner, leading also to lateral forces or vacuum torques.
Metamaterials: An interesting problem is to attempt to reverse the sign of the force. One
proposed method is to use cavities in which one side is a metamaterial, that is, a film with a
nanoscale patterning whose morphology can be used to control the dielectric function of
the surface. A common type of metamaterial is composed of nanoscale split ring resonators
(SRR’s) patterned into a gold film. The size of the resonators determines the frequency of
the optical resonance, which in turn determines the length-scale at which a Casimir
repulsion is expected to occur (this applies to all fields).
Liquids: Another possibility to reverse the sign of the Casimir force is to use a liquid
medium between the reflectors with a dielectric function lying between those of the two
reflectors. Members of the ESF network are actively researching new methods to measure
Casimir forces in liquids [2, 3]. Calculations of Casimir forces for the solid-liquid-solid
system using measured dielectric functions of all involved materials have shown that even
if the dielectric function is known over all relevant frequency ranges, the scatter in the
dielectric data can lead to a very large scatter in the calculated forces [3]. Furthermore, in
order to explore repulsive Casimir forces between solid materials with liquid as the
intervening medium, we analyzed dielectric data for a wide range of materials as, for
example, (p)olytetrafluoroethylene, polystyrene, silica, and more than 20 liquids [4].
Despite a significant variation in the dielectric data published from different sources, a
scheme was provided based on measured static dielectric constants, refractive indices, and
imposing Kramers-Kronig consistency to dielectric data to create accurate dielectric
functions at imaginary frequencies. The latter is necessary for more accurate force
calculations via the Lifshitz theory, allowing reliable predictions of repulsive Casimir
forces [4]. Finally, it was shown that even ultra thin nanometer thick liquid layers (1-2 nm
in thickness) can affect the Casimir force at short separations [5]. Studies are in progress to
understand the interplay of optical properties of the intervening liquid/interacting bodies
and surface roughness with respect to the sign of the Casimir force.
Phase change & dissimilar materials: A particularly exciting possibility is to produce a
‘switchable’ force by employing materials whose optical properties can be changed in situ
in response to a simple stimulus.
To obtain large Casimir force
contrast for a single material
(>20%) a significant modification
of its dielectric response is
required. Phase changing materials
(PCMs), which are commonly
used as active media in rewritable
optical disks (i.e. CD, DVD and
Blu-Ray), can provide large
The Casimir force is higher for crystalline than amorphous PCMs. The contribution of free electrons (Drude term) and the change of bonding to the Casimir force contrast suggest potential pathways to optimize force contrast for MEMS applications (Advanced. Funct.
Mat. 22, 3729, 2012)
25
modification in dielectric response by switching reversibly between an amorphous and a
crystalline phase. We recently demonstrated a significant change in the Casimir force when
switching between the two phases [6, 7]. Moreover, force measurements between Au-
semimetals (HOPG) plate and Au-conductive oxides (ITO) indicated strong force variation
[8,9,10]. The variation in the optical properties of the materials produces clearly observed
differences in the Casimir force as predicted by calculations based on the quantum theory
of optical networks and the Lifshitz theory [6-10]. Additionally, the Lifshitz formula for
dispersive forces was generalized to materials, which cannot be described with the local
dielectric response [11]. The principal nonlocality (spatial dispersion) of poor conductors is
related to the finite screening length of the penetrating field. The formula for the force
interpolates between good metals and dielectrics. Finally, the force in the nonequilibrium
configuration when interacting bodies have different temperatures was investigated [11,12].
This configuration opens up a variety of possibilities including the repulsive situation. All
these studies open new possibilities to control Casimir dispersion forces in micro/nano
devices for widespread applications.
Surfaces: The absolute distance separating two interacting bodies is a parameter of
principal importance for the determination of Casimir-Lifshitz forces [13, 14]. The absolute
distance becomes difficult to determine when the separation gap approaches nanometer
dimensions due to the presence of nanoscale surface roughness [13, 14]. In fact, when the
bodies are brought into gentle contact they are still separated by some distance d0, which
we call the distance upon contact due to surface roughness. d0 is important for MEMS
because stiction due to adhesion is a major failure mode. Furthermore, it plays an important
role in contact mechanics, in heat transfer, contact resistivity, lubrication, sealing, capillary
forces and wetting, where knowledge of d0 provides further insight of how adsorbed water
wets a rough surface. Using gold films as an example we demonstrated that [13] for two
parallel plates d0 is a function of the nominal size of the contact area L and gave a simple
expression for d0(L) via the surface roughness characteristics [13]. In the case of a sphere-
plate geometry, which is the most common in force measurements, the scale dependence
manifests itself as an additional uncertainty in the separation depending on the roughness of
interacting bodies and disappears in the limit of infinite large bodies. This effect has strong
implications for static and dynamic force measurement techniques with respect to the
obtained accuracy at short separations (<100 nm). Furthermore, we investigated the
influence of nanoscale surface roughness on the Casimir force and it was found that at
separations below 80 nm the roughness effect is manifested through a strong deviation from
the normal scaling of the force with separation distance. Moreover, deviations from
theoretical predictions based on perturbation theory can be larger than 100% [14] and work
is in progress on the theory to describe the
experimental force data with further
applications to MEM actuation dynamics.
Electrostatics patch effects of surfaces: The
surfaces of real metals are not equipotentials
but are rather described by a locally varying
surface voltage, known simply as patch
potentials. Patch potentials exist for several
reasons. One is that the work function of a
crystalline structure depends upon which
crystallographic plane an electron is extracted
from. Real metal surfaces are typically
composed of a network of crystallites with
random crystallographic orientations, thereby
Comparison of the residual pressure δPDrude
between the experimental pressure and the
Drude prediction with patch pressure Ppatch
for four different patch models [15]
Quasilocal model [15]
26
giving rise to a nonuniform potential over the metal’s surface. In addition, surface
contamination by adsorbates is well-known experimentally and theoretically to lead to
changes in the work function. Even for monocrystaline surfaces a spatially varying
potential has been observed. Patch potentials have important implications in various
experimental disciplines, including gravitational measurements on elementary charged
particles, tests of the general theory of relativity, ion trapping, and the physics of Rydberg
atoms .In any case electrostatic patch potentials give rise to forces between neutral
conductors at distances in the micrometer range and must be accounted for in the analysis
of Casimir force experiments [15, 16]. A quasilocal model for describing random potentials
on metallic surfaces have been developed. In contrast to some previously published results,
it is found that patches may provide a significant contribution to the measured signal and
thus may be a more important systematic effect than was previously anticipated.
Additionally, patches may render the experimental data at distances below 1 μm compatible
with theoretical predictions based on the Drude model [15]. Moreover, the exact solution
for the electrostatic patch interaction energy in the sphere-plane geometry used in force
measurements has been derived, including exact analytical formulas for the electrostatic
patch force and minimizing potential [16]. Once the patch potentials on both surfaces are
measured by dedicated experiments these formulas can be used to exactly quantify the
sphere-plane patch force in the particular experimental situation. Still work is in progress to
implement surface potential measurements with KPFM into patch potential contributions
[15, 16].
Representative references
[1] V.B. Svetovoy, P.J. van Zwol, G. Palasantzas,
J.Th.M. De Hosson, Phys. Rev. B 77, 035439 (2008).
[2] P. J. van Zwol, G. Palasantzas, and J. Th. M.
DeHosson, Phys. Rev. E 79, 041605 (2009)
[3] P. J. van Zwol, G. Palasantzas, and J. Th. M. De
Hosson, Phys. Rev. B 79, 195428 (2009)
[4] P. J. van Zwol and G. Palasantzas, Phys. Rev. A 81,
062502 (2010)
[5] G. Palasantzas, V. B. Svetovoy, and P. J. van Zwol,
Phys. Rev. B 79, 235434 (2009)
[6] G. Torricelli, P. J. van Zwol, O. Shpak, C. Binns, G.
Palasantzas, B. J. Kooi, V. B. Svetovoy, M. Wuttig, Phys.
Rev. A 82, 010101(R) (2010); Gauthier Torricelli, Peter
J. van Zwol, Olex Shpak, George Palasantzas, Vitaly B.
Svetovoy, Chris Binns, Bart J. Kooi, Peter Jost, and
Matthias Wuttig, Advanced Functional Materials, 22,
3729 (2012).
[7] NEW SCIENTIST: Casimir effect put to work as a
nano-switch / http://www.newscientist.com/article/dn19120-
casimir-effect-put-to-work-as-a-nanoswitch.html [8] G. Torricelli, I. Pirozhenko, S. Thornton, A.
Lambrecht and C. Binns, To appear in EPL (2011)
[9] G. Torricelli, S. Thornton, C. Binns, I. Pirozhenko
and A. Lambrecht , Journal of Vacuum Science &
Technology B: Microelectronics and Nanometer
Structures , 28, C4A30 (2010).
[10] S. de Man, K. Heeck, R. J. Wijngaarden, and D.
Iannuzzi, Phys. Rev. Lett. 103 040402 (2009)
[11] V.B. Svetovoy, Phys. Rev. Lett. 101, 163603 (2008).
[12] M. Antezza, L. P. Pitaevskii, S. Stringari, and V. B.
Svetovoy, Phys. Rev. A 77, 022091 (2008).
[13] P. J. van Zwol, V. B. Svetovoy, and G. Palasantzas,
Phys. Rev. B 80, 235401 (2009)
[14] P.J. van Zwol, G. Palasantzas, J. Th. M. DeHosson,
Phys. Rev. B B 77, 075412 (2008); P.J. van Zwol, G.
Palasantzas, M. van de Schootbrugge, J. Th. M. De
Hosson, Appl. Phys. Lett. 92, 054101 (2008).
PHYSICAL REVIEW A 86, 052509 (2012)
[15] R. O. Behunin, F. Intravaia, D. A. R. Dalvit, P.
A. Maia Neto, and S. Reynaud, PHYSICAL REVIEW
A 85, 012504 (2012)
[16] R. O. Behunin, Y. Zeng, D. A. R. Dalvit, and
S. Reynaud, Phys. Rev. A 86, 052509 (2012)
2. Casimir-Polder interaction (atoms, molecules) While interacting plates and spheres probe global properties of the quantum vacuum
interaction, atoms and molecules constitute local field probes and may provide access to
different information. The interaction between atoms and surfaces is normally called the
Casimir-Polder interaction and is actively studied by members of the network [1-9], including
its impact in far reaching topics such as interference between macro-molecules and quantum
decoherence. In general the atom surface interaction is relevant for
matter wave interferometry
atomic quantum reflection
electronic spectra of atoms close to surfaces
27
auto ionization of Rydberg atoms close to surfaces
modifications of trapping potentials for atoms on nanostructured surfaces
atomic surface sensors
The standard theory for the Casimir-Polder interaction assumes thermal equilibrium, yet in
some experimentally and technologically important situations this is not achieved. The theory
to describe such experimental situations is based on a non-equilibrium approach, allowing for
new phenomena such as heat transfer and ensuing repulsive forces. The Casimir Polder force
is also important for guiding and trapping molecules in ‘atom chips’. While an atom in its
ground state is very close to thermal equilibrium in ambient temperature since its excitation
energies are very large compared to thermal energies, this is not the case for molecules, which
can easily be excited by thermal photons. Ground state molecules are therefore typically
strongly out of thermal equilibrium and a fully non-equilibrium theory is required to describe
the resulting molecule-surface force.
Representative references
[1] A. D. Cronin, J. Schmiedmayer, et al. (2009).
Reviews of Modern Physics 81(3): 1051-1129.
[2] J. A. Crosse, S. A. Ellingsen, et al. (2010). Physical
Review A 82(2): 9902-9902.
[3] S. A. Ellingsen, S. Y. Buhmann, et al. (2010).
Physical Review Letters 104(22): 3003-3003.
[4] J. Schiefele, and C. Henkel (2010). Physical Review
A 82(2): 3605-3605.
[5] S. Scheel, and S. Y. Buhmann (2009). Physical
Review A 80(4): 2902-2902.
[6] A. Sambale, S. Y. Buhmann, et al. (2010). Physical
Review A 81(1): 2509-2509.
[7] F. Cornu and Ph. A. Martin, J. Phys. A. : Math.
Theor. 42 (2009) 495001
[8] R. Messina et al, Phys. Rev. A 80 (2009) 022119
[9] A. M. Contreras-Reyes et al, Phys. Rev. A 82 (2010)
052517
3. Thermal Casimir effect Thermal corrections to the Casimir force is a field of research bustling with activity [1-18]
also within our CASIMIR network. For more than 10 years, a discrepancy between precision
experiments and theoretical predictions using the Lifshitz theory for the Casimir force
between dissipative metallic plates has been a point of discussion. Although much research
has been made into the field, the thermal debate is still open, and no consensus has been
reached on an explanation for the discrepancy. We present in this section briefly the research
made into the temperature correction to the Casimir force, both on the experimental and
theoretical side, as well as the research made on the related (but less controversial) thermal
effects on the Casimir-Polder interaction between atoms and surfaces.
Experimental developments: On the experimental side, the year 2010 has been marked by
controversy as well as proposals for new experiments. Central to the developments in the
field of the thermal Casimir effect in 2010 was the group of Lamoreaux (USA) [1].
Remarkably, whereas the high precision experiments by Decca's group (USA) [2] agreed
with a non-dissipative theory of the Casimir interaction, the new experiment favours the
dissipative theory as it is to be expected on fundamental grounds. This discrepancy
between theory and experiment is rather puzzling and provokes differences in opinions
[3,4] as well as efforts towards possible resolutions. New methods are proposed for
Casimir data comparison with optical data by use of modified Kramers-Kronig relations.
The aim is to bypass the incomplete knowledge of optical properties of the metals
throughout the whole frequency range [5,6]. Suggestions for future experiments were
made in an effort to obtain further empirical evidence on this topic: experiment using a
torsion balance to measure the force between a cylinder and a plate [5]; study of the
Casimir force on bodies with ferromagnetic properties [6].
Theory developments: Important background theory was published concerning quantized
field commutators [7]. In light of propositions in previous years to measure the Casimir
effect across the superconducting phase transition in a metal, a simple method for
extending the superconducting permittivity to imaginary frequencies was also developed
28
[8]. Another theoretical point which has been a point of discussion for some time is the
point for the Casimir effect between perfectly pure and infinitely large metal plates
described by the celebrated Drude model, the associated entropy does not vanish at zero
temperature: the so-called Nernst heat theorem problem. This problem is not solved by
letting one of the bodies be spherical (as in most experimental situations [9]), but comes
only with the specific assumption of vanishing electronic relaxation at zero temperature.
Recently it was shown that the entropy anomaly could be interpreted as frozen bulk
currents in the materials resulting in a glass-like state whose non-vanishing entropy would
be expected [10]. Further evidence for the strong link between such "Foucault currents"
and the low-temperature Casimir entropy was provided [10] when it was shown that the
low temperature expansion of these currents alone can be identified with that of the full
Casimir interaction. Remarkable progress was also reported on the calculation of the
Casimir force at finite temperatures between metallic sphere and plate using different
models for the metals [11,12]. Nonmonotonous entropy behaviour was observed not only
for the Drude metal, but also for ideal and non-dissipative metallic permittivity models.
Casimir-Polder interaction: Another area where temperature effects play a major role is
the Casimir-Polder force between atoms and macroscopic bodies (see also sec. 2). In a
number of experimentally and technologically interesting configurations, the atoms or
particles are not in thermal equilibrium with their environment; examples include beams
of cold molecules, Bose-Einstein condensates and highly excited Rydberg atoms. The
Casimir-Polder potential on a Rydberg atom in a cavity was measured indirectly in [13],
and theoretical and a numerical calculation of Casimir-Polder forces on Rydberg atoms
was performed in [14]. It was shown that the potential acted on a non-equilibrium particle
sufficiently close to a metallic wall will be independent of temperature from absolute zero
to room temperature and beyond [15], which is a result of experimental importance to
such systems as cold molecules and Rydberg atoms close to bodies. A related calculation
on quantum reflection of non-equilibrium atoms was performed in [16].
Representative references
[1] A. O. Sushkov, W. J. Kim, D. A. R. Dalvit, S. K.
Lamoreaux, arXiv:1011.5219 (2010); W. J. Kim et al,
Physical Review A 81 (2010) 022505
[2] D. Decca, E. Fishbach, G.L. Klimchitskaya, D.E.
Krause, D. López, V. M. Mostepanenko, Physical
Review A 82 052515 (2010)
[3] S. Lamoreaux, Contribution to Springer Lecture
Notes in Physics, arXiv:1008.3640 (2010)
[4] G. L. Klimchitskaya and V. M. Mostepanenko,
arXiv:1010.2216 (2010)
[5] G. Bimonte, Physical Review A 81, 062501 (2010)
[6] G. Bimonte, arXiv:1012.1536 (2010)
[7] G. Bimonte, Journal of Physics A 43, 155402 (2010)
[8] G. Bimonte, H. Haakh, C. Henkel, F. Intravaia,
Journal of Physics A 43, 145304 (2010)
[9] M. Bordag, I. Pirozhenko, Physical Review D 82,
125016 (2010)
[10] F. Intravaia, S. Ellingsen, C. Henkel, Physical
Review A 82, 032504 (2010)
[11] A. Canaguier-Durand, P.A. Maia Neto, A.
Lambrecht, S. Reynaud, Physical Review Letters 104,
040403 (2010)
[12] A. Canaguier-Durand, P. M. Maia Neto, A.
Lambrecht, S. Reynaud, Physical Review A 82, 012511
(2010)
[13] H. Kübler, P. Shaffer, T. Baluktsian, R. Löw, T.
Pfau, Nature photonics 4 112 (2010)
[14] J. A. Crosse, S. A. Ellingsen, K. Clements, S. Y.
Buhmann, S. Scheel, Physical Review A 82, 010901(R)
(2010); 82, 029902(E) (2010)
[15] S. A. Ellingsen, S. Y. Buhmann, S. Scheel, Physical
Review Letters 104, 223003 (2010)
[16] V. Druzhinina, M. Mudrich, F. Arnecke, J.
Madroñero, A. Buchleitner, Physical Review A 82,
032714 (2010)
4. Dynamical Casimir effect This is a topic actively studied by members of the network. The so-called dynamical Casimir
effect should occur when the motion of the boundaries is performed with non-constant
acceleration, giving rise to dissipative phenomena, i. e. to photon production from the vacuum
[1]. A more general issue is the study of the quantum vacuum with moving boundary
conditions, allowing investigation of unsolved problems in quantum electrodynamics,
cosmology and general relativity. This subject has gained importance in the last decade
29
following precise experimental results in the measurement of the Casimir effect. Only one
accurate measurement of this effect was done using the original Casimir configuration of two
parallel plane metallic surfaces [2]. A new experiment has been proposed [7] where the
primary objective of this project is the experimental verification of this dissipation effect due
to the friction of the vacuum [3]. In principle the effect is possible also for a single mirror
oscillating in the sea of vacuum fluctuations, but the predicted number of photons produced is
immeasurably small for nonrelativistic mirror trajectories. Nonetheless there is an
experimental configuration which should allow production of an observable number of
photons: the mirror becomes the wall of a cavity and it oscillates at a frequency which is
twice the resonance frequency of the cavity itself (parametric resonance condition). Through
this mechanism, the number of produced photons should grow exponentially inside the cavity.
It has become evident that the number of photons inside the cavity depends on the product
between the number of oscillations performed by the moving boundary and a displacement
parameter, which measures the wall displacement amplitude. The inherent instability present
in shown expressions (number of produced photons would be sufficient, for large oscillation
times, to melt the cavity) was removed with different approaches [4]. The quantum nature of
the dynamical Casimir effect requires a specific theoretical study, whereas the previous
expressions for the number of photons produced are obtained in cavities with perfectly
conducting walls. Several theoretical papers have recently analysed the problem of photon
generation for the experimental scheme [5] of the Padova group, leading to the generation of a
few thousand photons within the present apparatus, even if the theoretical results are obtained
in different theoretical frameworks [6]. We have to mention that groups in Europe have
performed advanced experiments analogous to the dynamical Casimir effect [8] but it still
remains puzzling if an adiabatic moving boundary condition within an absorbing medium can
yield photons generated from genuine vacuum. These are issues to be further investigated into
the future.
Representative references
[1] S. A. Fulling and P. C. W. Davies, Proc. R. Soc.
London A 348 (1976) 393; A. Lambrecht, M.-T. Jaekel,
S. Reynaud, Phys. Rev. Lett. 77 (1996) 615
[2] G. Bressi, G. Carugno, R. Onofrio, and G. Ruoso,
Phys. Rev. Lett. 88 (2002) 041804
[3] R. Golestanian and M. Kardar, Phys. Rev. Lett. 78
(1997)
[4] Y. N. Srivastava, A. Widom, S. Sivasubramanian and
M. P. Ganesh, Phys. Rev. A 74 (2006) 32101; V. V.
Dodonov and A. V. Dodonov, J. Phys. A 39 (2006) 6271;
F. X. Dezael, A. Lambrecht, EPL 89 (2010) 14001
[5] M. Uhlmann, G. Plunien, R. Sch¨utzhold, and G. Soff,
Phys. Rev. Lett.,93, pp. 193601–4, 2004; V. V. Dodonov
and A. V. Dodonov, J. Phys B, 39, pp. S749–S766, 2006;
M. Crocce, D. A. R. Dalvit, and F. D. Mazzitelli, Phys.
Rev. A, 66, 2002; M. Crocce, D. A. R. Dalvit, F. C.
Lombardo, and F. D. Mazzitelli, Phys. Rev. A, 70, pp.
033811–6, 2004.
[6] E. Yablonovitch, Phys. Rev. Lett., 62, 1989; Y. E.
Lozovik, V. G. Tsvetus, and E. A. Vinogradov, Physica
Scripta, 52, pp. 184–190, 1995.
[7] G. Carugno, INFN, Research grant obtained from
Julian Schwinger Foundation (2011); see also Braggio C,
Bressi G, Carugno G, Del Noce C, Galeazzi G, Lombardi
A, Palmieri A, Ruoso G and Zanello D, Europhys. Lett.
70 754 (2005); Braggio C , Bressi G , Carugno G ,
Dodonov A V, Dodonov V V , Galeazzi G, Ruoso G and
Zanello D, Phys. Lett. A (2006); Braggio C, Bressi G,
Carugno G, Lombardi A, Palmieri A, Ruoso G and
Zanello D, Rev. Sci. Instrum. 75 4967 (2004).
[8]
C. M.Wilson, G. Johansson, A. Pourkabirian, M. Simoen,
J. R. Johansson, T. Duty, F. Nori, P. Delsing, Nature 479,
376 (2011); Pasi Lähteenmäki, G. S. Paraoanu, Juha
Hassel, and Pertti J. Hakonen, PNAS 1212705110
(2013).
5. Casimir effect in complex geometries and (MEMS) This is a topic actively studied by members of the network due to its importance in direct
technology applications [1-6]. MEMS have the right size for the Casimir force to exert itself.
This is because they have surface areas large enough and separation gaps small enough for the
force to draw components together and possibly lock them together, which is an effect known
as stiction. Such permanent adhesion (in addition to capillary adhesion due to the water layer
present on almost all surfaces) is a common cause of malfunction in MEMS. The components
in MEMS are designed to be very close to each other, where under the right circumstances
30
reaching separations of even a few nanometres during motion [1]. The Casimir force can
become significant and affect the operation of the device leading to pull-in instabilities and
eventually to stiction. Indeed, at 100 nm separations the Casimir force is comparable to an
electrostatic force of ~0.1 V, while at 10 nm it
is comparable to an electrostatic force of ~0.5
V. Typical actuation potentials in
MEMS/NEMS are 0.1-1 V. This explains
why there is interest in the Casimir force in
connection with micro/nanomechanics. The
growing relevance of the Casimir force to
current MEM devices requires its description
and calculation under realistic circumstances,
including surface roughness and proper
dielectric properties of real materials. In
practice, it is often difficult to know which
force is causing stiction; thus detailed
knowledge of the Casimir/VdW force is very
important.
Moreover, the study of Casimir force in complex MEM geometries and novel
topologies, such as patterned or corrugated surfaces, nanospheres or small spheroïdal shaped
bodies has become a highly active research area [2-5]. A specific nontrivial geometry that is
of particular interest for applications is that of surfaces with periodic corrugations [3-5]. As
lateral translation symmetry is broken, the Casimir force contains a lateral component, which
is smaller than the normal one but has been suggested as a method to achieve contactless
force transmission in a micromachine [2, 3]. Alternatively a vacuum torque arises when
breaking the rotational symmetry, that is, when the corrugations are not aligned.
Recently using the measured optical response and surface roughness topography as inputs,
realistic calculations were performed of the combined effect of Casimir and electrostatic
forces on the actuation dynamics of microelectromechanical systems (MEMS) [6]. In contrast
with the expectations, roughness can influence MEMS dynamics, even at distances between
bodies significantly larger than the root-mean-square roughness. This effect is associated with
statistically rare high asperities that can be locally close to the point of contact. It is found that
even though surface roughness appears to have a detrimental effect on the availability of
stable equilibria, it ensures that those equilibria can be reached more easily than in the case of
flat surfaces. Hence these findings play a principal role for the stability of microdevices such
as vibration sensors, switches, and other related MEM architectures operating at distances
below 100 nm. These were and still are topics of intense research within the CASIMIR
network.
Representative references
[1] J. Munday and F. Capasso, Nature 447, 772, (2007)
[2] A. Canaguier-Durand, P. A. Maia Neto, I. Cavero-
Pelaez, A. Lambrecht, S. Reynaud, Phys. Rev. Lett.102,
230404 (2009)
[3] R. B. Rodrigues, P. A. Maia Neto, A. Lambrecht, S.
Reynaud, Phys. Rev. Lett. 96, 100402 (2006); Physical
Review A 75, 062108 (2007).
[4] A. Ashourvan, M. Miri, and R. Golestanian, Phys.
Rev. Lett. 98, 140801 (2007)
[5] M. Miri and R. Golestanian, Appl. Phys. Lett. 92,
113103 (2008); M. Miri and R. Golestanian, J. Phys.:
Conf. Ser. 161, 012038 (2009).
[6] W. Broer, G. Palasantzas, and J. Knoester, Phys. Rev.
B 87, 125413 (2013).
6. Casimir effect in different geometries This is a topic actively studied by members of the network due to its high importance in
fundamental physics but also technology. Indeed, for a long time, the exact calculation of the
A MEMS device constructed to study the lateral
Casimir force between corrugates surfaces
31
Casimir force has been possible only for specific geometries such as the plane-plane geometry
initially considered by Casimir. For comparison with experiments usually done with the
plane-sphere geometry, one has thus been left with unsatisfactory approximate methods, such
as the proximity force approximation (PFA) proposed by Derjaguin in 1934. The method
takes the force density known from the plane parallel case and integrates it over the curved
surface. Clearly, this method works only for small deviations from the plane-plane geometry.
Furthermore, it is impossible to get higher order corrections or information on the precision of
the approximation. Due to the increasing precision of the measurements, there was a call to go
beyond the PFA. This call was matched by different methods.
The multiple scattering approach has recently been introduced for calculating the
Casimir force in cylinder-plane and in sphere-plane geometry [1,2,3]. This method has than
been applied in [4,5] to get an asymptotic expansion for small separation. In leading order, the
PFA is reproduced, the next order gives the first analytic correction beyond. For Dirichlet
boundary conditions, this result was nicely confirmed by the independent world line methods
in [6]. The numerical application of the scattering approach to small separation requires
significant computational effort. Agreement with the analytic method is found for Dirichlet
boundary conditions while the results diverge for Neumann boundary conditions and for the
electromagnetic case [7,8,9].
Special attention has been paid to the Casimir effect at finite temperature in
combination with a nontrivial geometry. Using the world line methods [10,11,12,13], it has
been found that at the power of the temperature may change in dependence on the geometry.
The problem of the violation of the third law of thermodynamics by the thermal Casimir force
was addressed in [14]. It was shown that it appears for specific models of a sphere in front of
a plane too excluding an explanation as infrared divergence.
Remarkable progress has been made in the study of the plane-sphere geometry taking
into account material dependence of the Casimir force [15,16,17,18]. A number of interesting
properties has been found in this study, like for example the existence of negative entropies
appearing already for lossless mirrors or the reduction of the difference between predictions
for plasma and Drude models.
Moreover, it became possible in the last few years to make significant progress in
calculating the force between plates showing corrugations [19,20]. When taking into account
the optical properties of the material, a good agreement with experiments is now obtained
[21]. A number of novel predictions have also been done for corrugated plates, for example
the torque for misaligned corrugations [22] or for a Bose-Einstein Condensate (BEC) close to
a corrugated plate [23], or the disorder appearing in vacuum and close to a rough plate [24].
Interesting effects also appear for atoms sitting above gratings [25,26].
Finally, another line of research has been to tackle the problem of arbitrarily shaped
surfaces by using finite-element numerical solution of field equations [27]. A number of
original predictions have been obtained by using such a method [28,29].
Representative references
[1] A. Lambrecht, P.A.M. Neto, and S. Reynaud. New J.
Phys., 8:243, 2006.
[2] A. Bulgac, P. Magierski, and A. Wirzba. Phys. Rev.
D, 73:025007, 2006.
[3] T. Emig, R. L. Jaffe, M. Kardar, and A. Phys. Rev.
Lett., 96(8):080403, 2006.
[4] M. Bordag and V. Nikolaev J. Phys. A: Math. Gen.,
41:164001, 2008.
[5] M. Bordag and V. Nikolaev. Phys.Rev.D, 81:065011,
2010.
[6] Holger Gies and Klaus Klingmuller. Phys. Rev.,
D74:045002, 2006.
[7] T.Emig. J. Stat. Mech., 08:P04007, 2008.
[8] P.A. Maia Neto, A. Lambrecht, and S. Reynaud.
Phys. Rev. A, 78:012115, 2008.
[9] F. C. Lombardo, F. D. Mazzitelli, and P. I. Villar.
Phys. Rev., D78:085009, 2008.
[10] Alexej Weber and Holger Gies. Phys. Rev. D,
80(6):065033, 2009.
[11] A. Weber and H. Gies. Phys. Rev. Lett.,
105(4):040403, 2010.
[12] H. Gies and A. Weber. Int. J. Mod. Phys.,
A25:2279–2292, 2010.
[13] K. Klingmuller and H. Gies. J. Phys., A41:164042,
2008.
[14] M. Bordag and I. G. Pirozhenko. Phys. Rev. D,
82:125016, 2010.
32
[15] A. Canaguier-Durand, P. A. Maia Neto, I. Cavero-
Pelaez, A. Lambrecht, and S. Reynaud. Phys.Rev.Lett.,
102:230404, 2009.
[16] A. Canaguier-Durand, P. A.Maia Neto, A.
Lambrecht, and S. Reynaud. Phys.Rev.Lett., 104:040403,
2010.
[17] A. Canaguier-Durand, P. A. Maia Neto, A.
Lambrecht, and S. Reynaud. Phys. Rev. A, 82(1):012511,
JUL 29 2010.
[18] A. Lambrecht, A. Canaguier-Durand, R. Guérout,
P.A. Maia Neto, and S. Reynaud. Casimir Physics, to
appear, 2010. arXiv:1006.2959.
[19] A. Lambrecht and V. N. Marachevsky. Phys. Rev.
Lett., 101(16):160403, 2008.
[20] A. Lambrecht. Nanotechnology - Shaping the void.
Nature, 454(7206):836, AUG 14 2008.
[21] Y. Bao, R. Guerout, J. Lussange, A. Lambrecht,
R.A. Cirelli, et al. Phys.Rev.Lett., 105:250402, 2010.
[22] R. B. Rodrigues, P. A. Maia Neto, A. Lambrecht,
and S. Reynaud. J. Phys. A: Math. Gen., 41(16):164019,
APR 25 2008.
[23] F. Impens, A. M. Contreras-Reyes, P.A. Maia Neto,
D.A.R. Dalvit, Romain Guérout, A. Lambrecht, and S.
Reynaud. Europhys. Lett., 92:40010, 2010.
[24] G.A. Moreno, R. Messina, D.A.R. Dalvit,
A. Lambrecht, P.A. Maia Neto, et al. Phys.Rev.Lett.,
105:210401, 2010.
[25] R. Messina, D. A. R. Dalvit, P. A. Maia Neto, A.
Lambrecht, and S. Reynaud. Phys. Rev. A, 80(2):022119,
2009.
[26] A. M. Contreras-Reyes, R. Guerout, P. A.Maia
Neto, D. A.R. Dalvit, A. Lambrecht, et al. Phys.Rev.,
A82:052517, 2010.
[27] M. T. Homer Reid, A. W. Rodriguez, J. White, and
S. G. Johnson. Phys. Rev. Lett., 103:040401, 2009.
[28] M. Levin, A. P. McCauley, A. W. Rodriguez,
M. T. Homer Reid, and S. G. Johnson. Phys. Rev. Lett.,
105:090403, 2010.
[29] A. W. Rodriguez, D. Woolf, A. P. McCauley, F.
Capasso, J. D. Joannopoulos, and S. G. Johnson. Phys.
Rev. Lett., 105:060401, 2010.
7. Casimir effect, Quantum vacuum and Cosmology This is a topic actively studied by members of the network due to its importance in frontier
fundamental problems related to understanding our cosmos [1-9]. Indeed, the Casimir effect
has a strong bearing on current problems in cosmology. Quantum theory states all modes of
the electromagnetic field have a zero-point energy of half a quantum, which if summed up to
a reasonable cut-off frequency, corresponds to a huge energy density. This energy density
should contribute to gravity as would any other source of energy provided that it fulfils the
Equivalence Principle. However its contribution is not observed. Einstein’s General Relativity
(GR) also predicts an intrinsic energy density of space (vastly smaller than the zero-point
energy), referred to as the cosmological constant (cc). The relationship between quantum
vacuum fluctuations and the cosmological constant is an open and intriguing question. Indeed,
the issue of the cosmological constant (cc) has got renewed thrust from the observational
evidence of acceleration in the expansion of our universe, first reported by two different
groups [10]. Another frontier of modern physics is the study of gravitational forces at small
length scales below 1 mm. Newton's inverse-square law of gravitation has been tested many
times at astronomical distances by observing the motion of planets. A number of groups are
now trying to verify the law at microscopic length scales with great precision. Such tests are
important because many theoretical models that attempt to unify the four fundamental forces
of nature predict the existence of previously undiscovered forces that would act at such scales,
where the Casimir force becomes dominant. Any deviation between experiment and theory
could hint at the existence of new forces. And even if there is agreement the measurements
would then put new limits on existing theories.
Thus, a very basic issue is if one is right in assuming that the vacuum energy satisfies
the equivalence principle of GR. In other words, how the renormalized Casimir energy of a
pair of plates couples to gravity? Zeta function regularization techniques have been
successfully used to understand these issues [11]. Topology also provides a mechanism
which, in a most natural way, permits to have a positive cc in a multi-supergraviton model
with anti-periodic fermions [12]. Another recent approach, involving for the moment scalar
fields, deals with the Casimir energy and force for a massive field with general curvature
coupling parameter, subject to Robin boundary conditions on two codimension-one parallel
plates, located on a (D + 1)-dimensional background spacetime with an arbitrary internal
space. The most general case of different Robin coefficients on separate plates has been
considered there. With independence of the geometry of the internal space, the Casimir forces
are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on
33
both plates and repulsive for Dirichlet boundary condition on one plate and Neumann
boundary condition on the other. For Robin boundary conditions, the Casimir forces can be
either attractive or repulsive, depending on the Robin coefficients and the separation between
the plates, what is actually remarkable (and useful). Indeed, research from members of the
network has demonstrated the existence of an equilibrium point for the interplate distance,
which is stabilized due to the Casimir force, and shown that stability is enhanced by the
presence of the extra dimensions. Applications of these properties in braneworld models were
given and the corresponding results were generalized to the geometry of a piston with
arbitrary cross section. Recently we have also considered a massive scalar field with an
arbitrary curvature coupling parameter in the region between two infinite parallel plates on
back- ground of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state
and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a
mode-summation method has been used, supplemented with a variant of the generalized
Abel-Plana formula. This has allowed to explicitly extract the contributions to the expectation
values which come from each single boundary, and to expand the second-plate-induced part
in terms of exponentially convergent integrals. Several limiting cases of interest have been
studied. The Casimir forces acting on the plates have been evaluated, and it has been seen that
the curvature of the background spacetime decisively influences the behaviour of these forces
at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature
coupling parameter and the mass of the field, two very different regimes are realized, which
exhibit monotonic and oscillatory behaviour of the vacuum expectation values, respectively.
The decay of the Casimir force at large plate separation is shown to be power-law (monotonic
or oscillating), with independence of the value of the field mass. A motivation for studying
these systems in cosmology is that if the universe, as it seems, is going to accelerate for ever,
standard cosmology will lead asymptotically to a dS universe. Another motivation is related
to the holographic duality known to hold between quantum gravity on dS spacetime and a
quantum field theory living on its boundary, identified with the timelike infinity surface of the
dS spacetime. In summary, this simplified set up already contains some basic ingredients that
more full-edged cosmological models will necessarily have to incorporate. We are on the way
to construct those, relying all the time on the most recent and accurate observational data.
Representative references
[1] M. Rypestol and I. Brevik: New J. Phys. 12, 013022
(2010).
[2] I. Brevik, O. Gorbunova and D. Saez-Gomez, General
Relativity and Gravitation 42, 1513 (2010).
[37] M. Rypestol and I. Brevik, Physica Scripta 82,
035101 (2010).
[4] I. Brevik, S. Nojiri, S. D. Odintsov and D. Saez-
Gomez, Eur. Phys. J. C 69, 563 (2010).
[5] K.A. Bronnikov and E. Elizalde, Physical Review
D81, 044032 (2010).
[6] E. Elizalde, A.A. Saharian, and T.A. Vardanyan,
Physical Review D81, 124003 (2010).
[7] E. Elizalde and J. Haro, Physical Review D81,
128701 (2010).
[8] Cosmology, the Quantum Vacuum, and Zeta
Functions: a Choice of Papers, Eds. V.V. Obukhov and
S.D. Odintsov (TSPU, Russia, 2010).
[9] Cosmology, Quantum Vacuum, and Zeta Functions,
Eds. D. Saez-Gomez, S.D. Odintsov and S. Xambo
(Springer Verlag, Berlin, 2011).
[10] S. Perlmutter et. al. [Supernova Cosmology Project
Collaboration], Astrophys. J. 517, 565 (1999); A.G. Riess
et. al. [Hi-Z Supernova Team Collaboration], Astron.
Journ. 116, 1009 (1998).
[10] E. Elizalde, S.D. Odintsov, A. Romeo, A.A.
Bytsenko and S. Zerbini, Zeta regularization techniques
with applications (World Scientific, Singapore, 1994); E.
Elizalde, Ten Physical Applications of Spectral Zeta
Functions (Springer-Verlag, Berlin, 1995).
[11] G. Cognola, E. Elizalde and S. Zerbini, Phys. Lett.
B624, 70 (2005); G. Cognola, E. Elizalde, S. Nojiri, S.D.
Odintsov and S. Zerbini, Mod. Phys. Lett. A19, 1435
(2004).
[12] E. Elizalde, S.D. Odintsov and A.A. Saharian, Phys.
Rev. D79, 065023 (2009)
34
Appendix 7.8: List of publications 2008-2013
*: Explicit reference to RNP CASIMIR in 111 publications
[1] C. J. Alberts, S. de Man, J. W. Berenschot, V. J. Gadgil, M. C. Elwenspoek and D. Iannuzzi.
Meas. Sci. Technol. 20, (2009) 034005.
[2] M. Antezza, L. P. Pitaevskii, S. Stringari and V. B. Svetovoy. Phys. Rev. A 77(2), (2008)
022091.
[3] C. J. Anthony, J. Bowen, G. Torricelli, E. L. Carter, M. C. L. Ward and C. Binns. Micro & Nano
Letters 3(1), (2008) 7.
[4] M. Arndt, T. Ju_mann and V. Vedral. HFSP Journal 3(6), (2009) 386.
[5] M. Arndt, M. Aspelmeyer and A. Zeilinger. Fortschritte der Physik- Progress of Physics 57,
(2009) 1153.
[6] M. Asorey and J. M. Munoz-Castaneda. J. Phys. A: Math. Gen. 41(16), (2008) 164043.
[7] M. Asorey and J. M. Munoz-Castaneda. J. Phys. A: Math. Gen. 41(30), (2008) 304004.
[8] A. Azari, H. S. Samanta and R. Golestanian. New J. Phys. 11, (2009) 093023. *.
[9] A. Azari, M. Miri and R. Golestanian. Phys. Rev. A 82(3), (2010) 032512.*.
[10] Y. Bao, R. Guerout, J. Lussange, A. Lambrecht, R. Cirelli et al. Phys.Rev.Lett. 105, (2010)
250402 *.
[11] G. Barton. New J. Phys. 12, (2010) 113044.
[12] G. Barton. New J. Phys. 12, (2010) 113045.
[13] G. Bimonte. Phys. Rev. A80, (2009) 042102. *.
[14] G. Bimonte, H. Haakh, C. Henkel and F. Intravaia. J. Phys. A 43, (2010) 145304 *.
[15] G. Bimonte. Phys. Rev. A81, (2010) 062501. *.
[16] M. Bordag and V. Nikolaev. J. Phys. A: Math. Gen. 41, (2008) 164001.
[17] M. Bordag and V. Nikolaev. J. Phys. A: Math. Gen. 42, (2009) 415203.*.
[18] M. Bordag, I. V. Fialkovsky, D. M. Gitman and D. V. Vassilevich. Phys.Rev.B 80, (2009)
245406. *.
[19] M. Bordag and I. Pirozhenko. Phys.Rev.D 81, (2009) 085023. *.
[20] M. Bordag and V. Nikolaev. Phys.Rev.D 81, (2010) 065011. *.
[21] M. Bordag and I. G. Pirozhenko. Phys. Rev. D 82, (2010) 125016. *, 1010.1217.
[22] I. Brevik, S. A. Ellingsen, J. S. Hoye and K. A. Milton. J. Phys. A: Math. Gen. 41(16), (2008)
164017.
[23] I. Brevik and K. A. Milton. Phys. Rev. E 78(1, Part 1), (2008) 011124.
[24] I. Brevik, S. A. Ellingsen and K. A. Milton. Phys. Rev. E 79(4, Part 1), (2009) 041120.
[25] I. Brevik and S. A. Ellingsen. Phys. Rev. A 79(2), (2009) 027801.
[26] I. Brevik, S. A. Ellingsen and K. A. Milton. Int. J. Mod. Phys. A 25(11), (2010) 2270.
[27] I. Brevik, O. Gorbunova and D. Saez-Gomez. General Relativity and Gravitation 42, (2010)
1513.
[28] K. A. Bronnikov, E. Elizalde and O. B. Zaslavskii. In P. Lavrov, editor, The problems of
modern cosmology, pages 114{124}. TSPU, Tomsk, Russia [2009]. *.
[29] K. A. Bronnikov and E. Elizalde. Phys. Rev. D 81, (2010) 044032. *.
[30] S. Y. Buhmann and S. Scheel. Phys. Rev. Lett. 100(25), (2008) 253201.
[31] S. Y. Buhmann and S. Scheel. Phys. Scripta T 135, (2008) 014013.
[32] S. Y. Buhmann, S. Scheel, H. Safari and D.-G. Welsch. Int. J. Mod. Phys. A 24(8-9), (2009)
1796.
[33] S. Y. Buhmann and S. Scheel. Phys. Rev. Lett. 102(14), (2009) 140404.
[34] S. Y. Buhmann, S. Scheel and J. Babington. Phys. Rev. Lett. 104(7), (2010) 070404.
35
[35] A. Canaguier-Durand, P. A. Maia Neto, I. Cavero-Pelaez, A. Lambrecht and S. Reynaud.
Phys.Rev.Lett. 102, (2009) 230404.
[36] A. Canaguier-Durand, P. A. M. Neto, A. Lambrecht and S. Reynaud. Phys. Rev. A 82(1),
(2010) 012511. *.
[37] A. Canaguier-Durand, P. A. Neto, A. Lambrecht and S. Reynaud. Phys.Rev.Lett. 104, (2010)
040403. *.
[38] W. B. Case, M. Tomandl, S. Deachapunya and M. Arndt. Optics Express 17(23), (2009)
20966.
[39] P.-O. Chapuis, S. Volz, C. Henkel, K. Joulain and J.-J. Grefet. Phys. Rev. B 77, (2008)
035431.
[40] G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov and S. Zerbini. Eur. Phys. J. C 64(3), (2009)
483. *.
[41] G. Cognola, E. Elizalde, S. Nojiri and S. D. Odintsov. The Open Astronomy Journal 79, (2009)
20. *.
[42] A. M. Contreras-Reyes, R. Guerout, P. A. Neto, D. A. Dalvit, A. Lambrecht et al. Phys.Rev.
A82, (2010) 052517. *.
[43] F. Cornu and P. A. Martin. J. Phys. A: Math. Gen. 42, (2009) 495001.*.
[44] J. A. Crosse, S. A. Ellingsen, K. Clements, S. Y. Buhmann and S. Scheel. Phys. Rev. A 82(1),
(2010) 010901. *.
[45] J. A. Crosse, S. A. Ellingsen, K. Clements, S. Y. Buhmann and S. Scheel. Phys. Rev. A 82(2),
(2010) 029902. *.
[46] D. A. R. Dalvit, P. A. Maia Neto, A. Lambrecht and S. Reynaud. J. Phys. A: Math. Gen.
41(16), (2008) 164028.
[47] D. A. R. Dalvit, P. A. Maia Neto, A. Lambrecht and S. Reynaud. Phys. Rev. Lett. 100(4),
(2008) 040405.
[48] T. David, Y. Japha, V. Dikovsky, R. Salem, C. Henkel and R. Folman. Eur. Phys. J. D 48,
(2008) 321.
[49] S. de Man, K. Heeck and D. Iannuzzi. Phys. Rev. A 79(2), (2009) 024102.*.
[50] F. X. Dezael and A. Lambrecht. Europhys. Lett. 89(1), (2010) 14001. *.
[51] V. Dikovsky, V. Sokolovsky, B. Zhang, C. Henkel and R. Folman. Eur. Phys. J. D 51, (2009)
247.
[52] B. Dobrich, H. Gies and M. DeKieviet. Nonperturbative access to Casimir- Polder forces
[2009]. ArXiv:0910.5889.
[53] A. Dreas-Wlodarczak, M. Muellneritsch, T. Juffmann, C. Cioffi, M. Arndt and M. Mayor.
Langmuir 26(13), (2010) 10822.
[54] C. Eberlein and R. Zietal. Phys. Rev. A 80(1), (2009) 012504.
[55] C. Eberlein and R. Zietal. Phys. Rev. A 82, (2010) 62506.
[56] E. Elizalde, S. D. Odintsov and A. A. Saharian. Phys. Rev. D 79(6), (2009) 065023. *.
[57] E. Elizalde and D. Saez-Gomez. Phys. Rev. D 80(4), (2009) 044030.
[58] E. Elizalde, A. A. Saharian and T. A. Vardanyan. Phys. Rev. D 81(12), (2010) 124003. *.
[59] S. A. Ellingsen, I. Brevik, J. S. Hoye and K. A. Milton. Phys. Rev. E 78(2, Part 1), (2008)
021117.
[60] S. A. Ellingsen. Phys. Rev. E 78(2, Part 1), (2008) 021120.
[61] S. A. Ellingsen. Europhys. Lett. 82(5), (2008) 53001.
[62] S. A. Ellingsen, S. Y. Buhmann and S. Scheel. Phys. Rev. A 79(5), (2009) 052903.
[63] S. A. Ellingsen, I. Brevik and K. A. Milton. Phys. Rev. E 80(2, Part 1), (2009) 021125.
[64] S. A. Ellingsen, S. Y. Buhmann and S. Scheel. Phys. Rev. A 80(2), (2009) 022901.
[65] S. A. Ellingsen, I. Brevik and K. A. Milton. Phys. Rev. D 81(6), (2010) 065031.
[66] S. A. Ellingsen, S. Y. Buhmann and S. Scheel. Phys. Rev. A 82(3), (2010) 032516. *.
[67] S. A. Ellingsen, S. Y. Buhmann and S. Scheel. Phys. Rev. Lett. 104(22), (2010) 223003. *.
36
[68] S. A. Ellingsen, Y. Sherkunov, S. Y. Buhmann and S. Scheel. In K. A. Milton and M. Bordag,
editors, Proceedings of the Ninth Conference on Quantum Field Theory Under the Influence of
External Conditions (QFEXT09), pages 168{177. World Scientific, New Jersey (2010).
[69] T. Emig and R. L. Jaffe. J. Phys. A: Math. Gen. 41(16), (2008) 164001.
[70] T. Emig, N. Graham, R. L. Jaffe and M. Kardar. Phys. Rev. D 77(2), (2008) 025005.
[71] T. Emig. Journal oF Statistical Mechanics-Theory and Experiment page P04007.
[72] T. Emig, N. Graham, R. L. Jaffe and M. Kardar. Phys. Rev. A 79(5), (2009) 054901.
[73] T. Emig. Int. J. Mod. Phys. A 25(11), (2010) 2177.
[74] R. Esquivel-Sirvent. Phys. Rev. A 77, (2008) 042107.
[75] R. Esquivel-Sirvent and L. I. Reyes-Galindo. Eur. Phys. Lett. 84, (2008) 48002.
[76] R. Esquivel-Sirvent, M. Palomino-Ovando and G. H. Cocoletzi. Appl. Phys. Lett. 95, (2009)
051909.
[77] R. Esquivel-Sirvent. J. of Phys. Conf. Ser. 161, (2009) 012012.
[78] R. Esquivel-Sirvent, G. H. Cocoletzi and M. Palomino-Ovando. J. Appl. Phys. 108, (2010)
114101.
[79] R. Esquivel-Sirvent. J. Chem. Phys. 132, (2010) 194707.
[80] R. Esquivel-Sirvent, G. H. Cocoletzi and M. Palomino-Ovando. In Quantum Field Theory
Under the Influence of External Conditions (QFExt09), page 249. World Scientific [2010].
[81] C. Genet, A. Lambrecht and S. Reynaud. European Physical Journal-Special Topics 160,
(2008) 183.
[82] S. Gerlich, M. Gring, H. Ulbricht, K. Hornberger, J. Tuexen, M. Mayor and M. Arndt.
Angewandte Chemie-International Edition 47(33), (2008) 6195.
[83] H. Gies and A. Weber. Int. J. Mod. Phys. A25, (2010) 2279. *.
[84] R. Golestanian. Phys. Rev. A 80(1), (2009) 012519.
[85] N. Graham, A. Shpunt, T. Emig, S. J. Rahi, R. L. Jaffe and M. Kardar. Phys. Rev. D 81(6),
(2010) 061701.
[86] M. Gring, S. Gerlich, S. Eibenberger, S. Nimmrichter, T. Berrada, M. Arndt, H. Ulbricht, K.
Hornberger, M. Mueri, M. Mayor, M. Boeckmann and N. L. Doltsinis. Phys. Rev. A 81(3), (2010)
031604.
[87] A. Alonso-Izquierdo, M. A. G. Leon, J. M. Guilarte and M. de la Torre Mayado. JHEP 1008,
(2010) 111.
[88] J. Guilarte, J. Munoz-Castaneda and M. Senosiain. Mathematical Physics and Field Theory
PUZ June 2009, (2009) 277.
[89] J. M. Guilarte and J. M. Munoz-Castaneda. Double-delta potentials: one dimensional
scattering. The Casimir effect and kink uctuations [2010]. To be published in the International
Journal of Theoretical Physics, arXiv:1010.3116.
[90] H. Haakh, F. Intravaia, C. Henkel, S. Spagnolo, R. Passante, B. Power and F. Sols. Phys. Rev.
A 80, (2009) 062905.
[91] H. Haakh, F. Intravaia and C. Henkel. Phys. Rev. A 82, (2010) 012507. *.
[92] H. Haakh, F. Intravaia and C. Henkel. In K. A. Milton and M. Bordag, editors, Quantum Field
Theory Under the Inuence of External Conditions (QFEXT09), pages 194{98. World Scientific
[2010]. *.
[93] C. Henkel and B. Horovitz. Phys. Rev. A 78, (2008) 042902.
[94] C. Henkel. In J. Reichel and V. Vuletic, editors, Atom chips. Wiley-VCH, Weinheim [2011].
[95] K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermueller, S. Nimmrichter, I. V. Goldt, O.
Boltalina and M. Arndt. New J. Phys. 11, (2009) 043032.
[96] J. S. Hoye, I. Brevik, S. A. Ellingsen and J. B. Aarseth. Phys. Rev. E 77(2, Part 1), (2008)
023102.
[97] J. S. Hoye and I. Brevik. Phys. Rev. E 80(1, Part 1), (2009) 011104.
[98] F. Impend, A. M. Contreras-Reyes, P. Maia Neto, D. Dalvit, R. Gurout, A. Lambrecht and S.
Reynaud. Europhys. Lett. 92, (2010) 40010. *.
[99] G.-L. Ingold, A. Lambrecht and S. Reynaud. Phys.Rev. E80, (2009) 041113. *.
37
[100] F. Intravaia and C. Henkel. J. Phys. A: Math. Gen. 41, (2008) 164018. Special issue
conference QFEXT (Leipzig Sep 2007).
[101] F. Intravaia and C. Henkel. Phys. Rev. Lett. 103, (2009) 130405. *.
[102] F. Intravaia, S. A. Ellingsen and C. Henkel. Phys. Rev. A 82, (2010) 032504. *.
[103] F. Intravaia and C. Henkel. In K. A. Milton and M. Bordag, editors, Quantum Field Theory
Under the Influence of External Conditions (QFEXT09), pages 199{203. World Scientific [2010].
*.
[104] F. Intravaia, C. Henkel and M. Antezza. In D. Dalvit, P. Milonni, D. Roberts and F. da Rosa,
editors, Casimir physics, Lecture Notes in Physics. Springer [2011]. ArXiv:1010.3046.
[105] G. Jourdan, A. Lambrecht, F. Comin and J. Chevrier. Europhys. Lett. 85(3), (2009) 31001.
[106] T. Juffmann, S. Truppe, P. Geyer, A. G. Major, S. Deachapunya, H. Ulbricht and M. Arndt.
Phys. Rev. Lett. 103(26), (2009) 263601.
[107] S. Kawka and B. A. van Tiggelen. Europhys. Lett. 89(1), (2010) 11002.
[108] V. V. Klimov and A. Lambrecht. Plasmonics 4(1), (2009) 31.
[109] K. Klingmuller and H. Gies. J. Phys. A41, (2008) 164042. 0710.4473.
[110] A. Lambrecht and I. Pirozhenko. Phys.Rev. A78, (2008) 062102.
[111] A. Lambrecht and V. N. Marachevsky. Phys. Rev. Lett. 101(16), (2008) 160403.
[112] A. Lambrecht. Nature 454(7206), (2008) 836.
[113] A. Lambrecht, A. Canaguier-Durand, R. Gurout, P. Maia Neto and S. Reynaud. Casimir
Physics, to appear ArXiv:1006.2959 *.
[114] J. Marino and R. Passante. In K. Milton and M. Bordag, editors, Quantum Field Theory under
the Influence of External Conditions (QFEXT09), page 328. World Scientific, Singapore [2010]. *.
[115] M. Marksteiner, P. Haslinger, H. Ulbricht, M. Sclafani, H. Oberhofer, C. Dellago and M.
Arndt. Journal of the American Society for Mass Spectrometry 19(7), (2008) 1021.
[116] M. Marksteiner, A. Divochiy, M. Sclafani, P. Haslinger, H. Ulbricht, A. Korneev, A.
Semenov, G. Gol'tsman and M. Arndt. Nanotechnology 20, (2009) 455501.
[117] M. Marksteiner, P. Haslinger, M. Sclafani, H. Ulbricht and M. Arndt.
Journal of Physical Chemistry A 113(37), (2009) 9952.
[118] R. Messina, R. Passante, L. Rizzuto, S. Spagnolo and R. Vasile. J. Phys. A: Math. Gen. 41,
(2008) 164031.
[119] R. Messina, D. A. R. Dalvit, P. A. Maia Neto, A. Lambrecht and S. Reynaud. Phys. Rev. A
80(2), (2009) 022119.
[120] R. Messina, R. Vasile and R. Passante. Phys. Rev. A 82, (2010) 062501.*.
[121] K. A. Milton, J. Wagner, P. Parashar and I. Brevik. Phys. Rev. D 81(6), (2010) 065007.
[122] M. Miri and R. Golestanian. Appl. Phys. Lett. 92(11), (2008) 113103.
[123] M. Miri, V. Nekouie and R. Golestanian. Phys. Rev. E 81(1, Part 2), (2010) 016104. *.
[124] G. Moreno, R. Messina, D. Dalvit, A. Lambrecht, P. Maia Neto et al. Phys.Rev.Lett. 105,
(2010) 210401. *.
[125] P. A. M. Neto, A. Lambrecht and S. Reynaud. Phys. Rev. A 78(1), (2008) 012115.
[126] S. Nimmrichter, K. Hornberger, H. Ulbricht and M. Arndt. Phys. Rev. A 78(6, Part B), (2008)
063607.
[127] S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch and M. Arndt. New J. Phys. 12,
(2010) 083003.
[128] L. Novotny and C. Henkel. Opt. Lett. 33, (2008) 1029.
[129] V. Obukhov and S. Odintsov, editors. Cosmology, the Quantum Vacuum, and Zeta Functions:
a Choice of Papers. A volume in honor of Professor Emilio Elizalde on the occasion of his 60th
birthday. TSPU, Russia [2010].
[130] S. Odintsov, E. Elizalde and O. Gorbunova, editors. The Casimir Effect and Cosmology. A
volume in honour of Professor Iver H. Brevik on the occasion of his 70th birthday. TSPU, Tomsk,
Russia [2009].
[131] G. Palasantzas, P. J. van Zwol and J. T. M. De Hosson. Appl. Phys. Lett. 93(12), (2008)
121912.
38
[132] G. Palasantzas, V. B. Svetovoy and P. J. van Zwol. Phys. Rev. B 79(23), (2009) 235434.
[133] G. Palasantzas. New Scientist (02 July 2010). *.
[134] I. Pirozhenko and A. Lambrecht. J.Phys.A A41, (2008) 164015.
[135] I. Pirozhenko and A. Lambrecht. Phys.Rev. A77, (2008) 013811.
[136] I. Pirozhenko and A. Lambrecht. Phys.Rev. A80, (2009) 042510. *, 0908.2351.
[137] L. P. Pitaevskii. Phys. Rev. Lett. 101, (2008) 163202.
[138] L. P. Pitaevskii. Laser Physics 19(4), (2009) 632.
[139] L. P. Pitaevskii. Phys. Rev. Lett. 102, (2009) 189302.
[140] L. P. Pitaevskii. Int. J. Mod. Phys. A 25(11), (2010) 2313. *.
[141] S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Ja_e, S. G. Johnson and M. Kardar. Phys. Rev. A
77(3), (2008) 030101.
[142] S. J. Rahi, T. Emig, R. L. Ja_e and M. Kardar. Phys. Rev. A 78(1), (2008) 012104.
[143] S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe and M. Kardar. Phys. Rev. D 80(8), (2009)
085021.
[144] S. J. Rahi, M. Kardar and T. Emig. Phys. Rev. Lett. 105(7), (2010) 070404.
[145] A. M. C. Reyes and C. Eberlein. Phys. Rev. A 79(4, Part B), (2009) 043834.
[146] A. M. C. Reyes and C. Eberlein. Phys. Rev. A 80(3), (2009) 032901.
[147] S. Reynaud, P. A. M. Neto and A. Lambrecht. J. Phys. A: Math. Gen. 41(16), (2008) 164004.
[148] S. Reynaud, A. Canaguier-Durand, R. Messina, A. Lambrecht and P. Neto. Int.J.Mod.Phys.
A25, (2010) 2201. *.
[149] R. B. Rodrigues, P. A. Maia Neto, A. Lambrecht and S. Reynaud. J. Phys. A: Math. Gen.
41(16), (2008) 164019.
[150] P. Rodriguez-Lopez, S. J. Rahi and T. Emig. Phys. Rev. A 80(2), (2009) 022519.
[151] L. Rosa and A. Lambrecht. Phys. Rev. D 82, (2010) 065025. *.
[152] E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier and J.-J. Greffet. Nature
Photonics 3(9), (2009) 514.
[153] M. Rypestol and I. Brevik. Phys. Scr. 82, (2010) 035101.
[154] M. Rypestol and I. Brevik. New J. Phys. 12, (2010) 013022.
[155] D. Sáez-Gómez, S. Odintsov and S. Xambó, editors. Cosmology, Quantum Vacuum, and Zeta
Functions. Springer-Verlag [2011].
[156] H. Safari, D.-G. Welsch, T. D. Ho and S. Y. Buhmann. Phys. Rev. A 77(5), (2008) 053824.
[157] H. Safari, D.-G. Welsch, S. Y. Buhmann and S. Scheel. Phys. Rev. A 78(6), (2008) 062901.
[158] A. Sambale, D.-G. Welsch, D. T. Ho and S. Y. Buhmann. Phys. Rev. A 78(5), (2008) 053828.
[159] A. Sambale, D.-G. Welsch, T. D. Ho and S. Y. Buhmann. Phys. Rev. A 79(2), (2009) 022903.
[160] A. Sambale, S. Y. Buhmann, D.-G. Welsch and T. D. Ho. Phys. Rev. A 80(5), (2009)
051801(R).
[161] A. Sambale, S. Y. Buhmann, T. D. Ho and D.-G. Welsch. Phys. Scripta T 135, (2009)
015019.
[162] A. Sambale, S. Y. Buhmann and S. Scheel. Phys. Rev. A 81(1), (2010) 012509. *.
[163] A. Sambale, D.-G. Welsch, S. Y. Buhmann and T. D. Ho. Opt. Spectrosc. (USSR) 108(3),
(2010) 391.
[164] S. Scheel and S. Y. Buhmann. Acta Physica Slovaca 58(5), (2008) 675.
[165] S. Scheel and S. Y. Buhmann. Phys. Rev. A 80(4), (2009) 042902.
[166] J. Schiefele and C. Henkel. J. Phys. A 42, (2009) 045401. *.
[167] J. Schiefele and C. Henkel. Phys. Rev. A 82, (2010) 023605.
[168] A. Siria, S. Huant, G. Auvert, F. Comin and J. Chevrier. Nanoscale Research Letters 5(8),
(2010) 1360.
[169] A. Stefanov, M. Berninger and M. Arndt. Measurement Science & Technology 19(5), (2008)
055801.
[170] V. B. Svetovoy. Phys. Rev. A 76(6), (2007) 062102.
[171] V. B. Svetovoy, P. J. van Zwol, G. Palasantzas and J. T. M. De Hosson. Phys. Rev. B 77(3),
(2008) 035439.
39
[172] V. B. Svetovoy. Phys. Rev. Lett. 101(16), (2008) 163603.
[173] V. B. Svetovoy. Phys. Rev. Lett. 102(21), (2009) 219903.
[174] G. Torricelli, S. Thornton, C. Binns, I. Pirozhenko and A. Lambrecht. Journal of Vacuum
Science & Technology B 28(3).
[175] G. Torricelli, P. J. van Zwol, O. Shpak, C. Binns, G. Palasantzas, B. J. Kooi, V. B. Svetovoy
and M. Wuttig. Phys. Rev. A 82(1), (2010) 010101.*.
[176] J. Tuexen, S. Gerlich, S. Eibenberger, M. Arndt and M. Mayor. Chemical Communications
46(23), (2010) 4145.
[177] H. Ulbricht, M. Berninger, S. Deachapunya, A. Stefanov and M. Arndt. Nanotechnology
19(4), (2008) 045502.
[178] B. A. van Tiggelen. Eur. Phys. J. D 47(2), (2008) 261.
[179] B. A. van Tiggelen and G. L. J. A. Rikken. Phys. Rev. Lett. 100(24), (2008) 248902.
[180] P. J. van Zwol, G. Palasantzas, M. van de Schootbrugge, J. T. M. de Hosson and V. S. J.
Craig. Langmuir 24(14), (2008) 7528.
[181] P. J. van Zwol, G. Palasantzas and J. T. M. De Hosson. Phys. Rev. B 77(7), (2008) 075412.
[182] P. J. van Zwol, G. Palasantzas and J. T. M. De Hosson. Phys. Rev. E 78(3, Part 1), (2008)
031606.
[183] P. J. van Zwol, G. Palasantzas, M. van de Schootbrugge and J. T. M. De Hosson. Appl. Phys.
Lett. 92(5), (2008) 054101.
[184] P. J. van Zwol, G. Palasantzas and J. T. M. DeHosson. Phys. Rev. E 79(4, Part 1), (2009)
041605.
[185] P. J. van Zwol, G. Palasantzas and J. T. M. De Hosson. Phys. Rev. B 79(19), (2009) 195428.
[186] P. J. van Zwol, V. B. Svetovoy and G. Palasantzas. Phys. Rev. B 80(23), (2009) 235401. *.
[187] P. J. van Zwol and G. Palasantzas. Advanced Science Letters 3(4), (2010) 358. *.
[188] P. J. van Zwol and G. Palasantzas. Phys. Rev. A 81(6), (2010) 062502.*.
[189] P. J. van Zwol and G. Palasantzas. Acta Phy. Pol. A 117(2), (2010) 379.
[190] P. van Zwol, V. Svetovoy and G. Palasantzas. In D. Dalvit, P. Milonni, D. Roberts and F. da
Rosa, editors, Casimir physics. Lecture Notes in Physics. Springer [2011]. ArXiv:1101.2224v1.
[191] R. Vasile and R. Passante. Phys. Rev. A 78, (2008) 032108.
[192] R. Vasile, R. Messina and R. Passante. Phys. Rev. A 79, (2009) 062106.
[193] A. Weber and H. Gies. Phys. Rev. D 80(6), (2009) 065033.
[194] A. Weber and H. Gies. Phys. Rev. D82, (2010) 125019. *.
[195] A. Weber and H. Gies. Phys. Rev. Lett. 105(4), (2010) 040403. *.
[196] S. Zaheer, S. J. Rahi, T. Emig and R. L. Jaffe. Phys. Rev. A 81(3), (2010) 030502.
[197] S. Zaheer, S. J. Rahi, T. Emig and R. L. Jaffe. Phys. Rev. A 82(5), (2010) 052507.
[198] R. Zandi, T. Emig and U. Mohideen. Phys. Rev. B 81(19), (2010) 195423.
[199] P. Zuurbier, S. de Man, G. Gruca, K. Heeck, and D. Iannuzzi, New J. Phys. 13, 023027
(2011)
[200] M. Schafer, I.Huet and H.Gies, Int.J. Mod. Phys. Conf. Ser. 14, 511 (2012)
[201] Bruno Bellomo, Riccardo Messina, Didier Felbacq, Mauro Antezza, Phys. Rev. A 87, 012101
(2013)
[202] Riccardo Messina, Mauro Antezza, Philippe Ben-Abdallah, Phys. Rev. Lett. 109, 244302
(2012)
[203] Bruno Bellomo, Riccardo Messina, Mauro Antezza, Europhys. Lett. 100, 20006 (2012)
[204] Riccardo Messina, Mauro Antezza, Phys. Rev. A 84, 042102 (2011)
[205] Riccardo Messina, Mauro Antezz, Europhys. Lett. 95, 61002 (2011)
[206] *Simen A. Ellingsen, Stefan Yoshi Buhmann, and Stefan Scheel, Phys. Rev. A 84, 060501(R)
(2011)
[207] *Simen A. Ellingsen, Stefan Yoshi Buhmann, and Stefan Scheel, Phys. Rev. A 85, 022503
(2012)
[208] *Stefan Yoshi Buhmann, Stefan Scheel, Simen A. Ellingsen, Klaus Hornberger, and [209]
Andreas Jacob, Phys. Rev. A 85, 042513 (2012)
40
[210] David T Butcher, Stefan Yoshi Buhmann, and Stefan Scheel, New J. Phys. 14 113013 (2012)
[211] Stefan Yoshi Buhmann, Hassan Safari, Stefan Scheel, and A. Salam, Phys. Rev. A 87,
012507 (2013)
[212] M. Tröndle, O. Zvagolskaya, A. Gambassi, D. Vogt, L. Harnau, C. Bechinger, and S.
Dietrich, Mol. Phys. 109, 1169 (2011).
[213] U. Nellen, J. Dietrich, L. Helden, S. Chodankar, K. Nygard, J. F. v. d. Veen, and C.
Bechinger, Soft Matter 7, 5360 (2011).
[214] Simen Å. Ellingsen, Stefan Yoshi Buhmann, and Stefan Scheel, Phys. Rev. A 060501(R)
(2011)
[215] Simen Å. Ellingsen, Stefan Yoshi Buhmann and Stefan Scheel, Phys. Rev. A 85, 022503
(2012).
[216] Mathias Boström,Clas Persson, Drew F. Parsons, Simen Å. Ellingsen, and Bo E. Sernelius,
EPL 101 43002 (2013).
[217] J. S. Høye and I. Brevik: II. European Phys. J. D 61, 335-339 (2011).
[218] K. A. Milton, E. K. Abalo, P. Parashar, N. Pourtolami, I. Brevik and S. A. Ellingsen: Phys.
Rev. A 83, 062507 (2011).
[219] J. S. Høye and I. Brevik: Europ. Phys. J. D 64, 1-3 (2011).
[220] K. A. Milton, P. Parashar, N. Pourtolami and I. Brevik: Phys. Rev. D 85, 025008 (2012).
[221] M. Bostrom, Bo E. Sernelius, I. Brevik and B. W. Ninham: Phys. Rev. A 85, 010701(R)
(2012).
[222] J. S. Høye and I. Brevik: Eur. Phys. J. D 66, 149 (2012).
[223] J. S. Høye and I. Brevik: Int. J. Mod. Phys. A 27, 1260011 (2012)
[224] K. A. Milton, E. K. Abalo, P. Parashar, N. Pourtolami, I. Brevik and S. ˚A. Ellingsen: Int. J.
Mod. Phys. A 27, 1260014 (2012).
[225] M. Bostrom, S. ˚A. Ellingsen, I. Brevik, D. F. Parsons and Bo E. Sernelius, Subtle
dependence on dielectric properties. Phys. Rev. A 85, 064501 (2012)
[226] M. Bostrom, B. W. Ninham, I. Brevik, C. Persson, D. F. Parsons and Bo E. Sernelius: Appl.
Phys. Lett. 100, 253104 (2012).
[227] M. Bostrom, I. Brevik, Bo E. Sernelius, H. Dou, C. Persson and B. W. Ninham: Phys. Rev. A
86, 014701 (2012).
[228] I. Brevik: J. Phys. A: Math. Theor. 45, 374003 (2012).
[229] K. A. Milton, E. K. Abalo, P. Parashar, N. Pourtolami, I. Brevik and S. ˚A. Ellingsen: J. Phys.
A: Math. Theor. 45, 374006 (2012) (21 pages).
[230] M. Bostrom, S. ˚A. Ellingsen, I. Brevik, M. Dou, C. Persson and Bo E. Sernelius: Europ.
Phys. J. B 85, 377 (2012).
[231] K. A. Milton, I. Brevik and S. ˚A. Ellingsen: Phys. Scripta T151, 014070 (2012).
[232] G. Bimonte, T. Emig, M. Kruger, M. Kardar, Phys. Rev. A 84, 042503 (2011).
[233] E. Noruzifar, T. Emig, R. Zandi, Phys. Rev. A 84, 042501 (2011).
[234] M. Kruger, T. Emig, G. Bimonte, M. Kardar, EPL 95, 21002 (2011).
[235] N. Graham, A. Shpunt, T. Emig, S. J. Rahi, R. L. Jaffe, M. Kardar, Phys. Rev. D 83, 125007
(2011).
[236] Matthias Kruger, Thorsten Emig, Mehran Kardar, Phys. Rev. Lett. 106, 210404 (2011).
[237] M. F. Maghrebi, S. J.Rahi, T. Emig, N. Graham, R. L. Jaffe, M. Kardar, PNAS 108, 6867
(2011).
[238] *G. Bimonte, T. Emig, Phys. Rev. Lett. 109, 160403 (2012).
[239] *M. Kruger, G. Bimonte, T. Emig and M. Kardar, Phys. Rev. B 86, 115423 (2012).
[240] E. Noruzifar, T. Emig, U. Mohideen, R. Zandi, Phys. Rev. B 86, 115449 (2012).
[241] P. Rodriguez-Lopez, T. Emig, Phys. Rev. A 85, 032510 (2012).
[242] *G. Bimonte, T. Emig, M. Kardar, Appl. Phys. Lett. 100, 074110 (2012).
[243] *G. Bimonte, T. Emig, R. L. Jaffe, M. Kardar, EPL 97, 50001 (2012).
[244] Allocca, Annalisa; Bimonte, Giuseppe; Born, Detlef; et al., JOURNAL OF
SUPERCONDUCTIVITY AND NOVEL MAGNETISM Volume: 25, 2557-2565 (2012)
41
[245] Bimonte, G.; Klimchitskaya, G. L.; Mostepanenko, V. M., PHYSICAL REVIEW A 84,
036501 (2011)
[246] Bimonte, Giuseppe, PHYSICAL REVIEW A 83 (2011)
[247] *A.A. Bytsenko and E. Elizalde, European Physical Journal C71, 1592 (2011).
arXiv:1105.0309 [hep-th]
[248] *G. Cognola, E. Elizalde, L. Sebastiani, and S. Zerbini, Physical Review D83, 063003 (2011).
arXiv:1007.4676 [hep-th]
[248] *E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, and S. Zerbini, Physical Review D83,
086006 (2011). arXiv:1012.2280 [hep-th]
[249] *E. Elizalde, S.D. Odintsov, and A.A. Saharian, Physical Review D83, 105023 (2011).
arXiv:1102.2202 [hep-th]
[250] J. Haro, J. Amors and E. Elizalde, Physical Review D83, 123528 (2011).
[251] S. Carloni, E. Elizalde, and P.J. Silva, Classical and Quantum Gravity 28, 195002 (2011).
arXiv:1009.5319 [hep-th]
[252] *Brevik, E. Elizalde, S. Nojiri, and S.D. Odintsov, Physical Review D 84, 103508 (2011).
arXiv:1107.4642 [hep-th]
[253] A.J. Lpez-Revelles and E. Elizalde, General Relativity and Gravitation 44, 751 (2012).
arXiv:1104.1123 [hep-th]
[254] E. Elizalde, S.D. Odintsov, L. Sebastiani, and S. Zerbini, European Physical Journal C72,
1843 (2012). arXiv:1108.6184 [hep-th]
[255] J. de Haro and E. Elizalde, Physical Review Letters 108, 061303 (2012).
[256] E. Elizalde, E.O. Pozdeeva and S.Yu. Vernov, Physical Review D85, 044002 (2012).
arXiv:1110.5806 [astro-ph.CO]
[256] *E. Elizalde and V. Skalozub, European Physical Journal C72, 1968 (2012).
arXiv:1202.3895, arXiv:1106.4962 [hep-th]
[257] J. de Haro, J. Amors and E. Elizalde, Physical Review D85, 123527 (2012). arXiv:1204.4039
[gr-qc]
[258] E. Elizalde and P.J. Silva, Journal of High Energy Physics 2012, 49 (2012). arXiv:1110.0036
[hep-th]
[259] E. Elizalde, L. Bonora and A. Bytsenko, Journal of Physics A: Mathematical and Theoretical
A45, 374002 (2012). arXiv:1206.0664 [hep-th]
[260] J. de Haro, J. Amors and E. Elizalde, Physical Review D86, 083528 (2012). arXiv:1206.6948
[gr-qc]
[261] *G. Cognola, E. Elizalde, L. Sebastiani, and S. Zerbini, Physical Review D86, 104046 (2012).
arXiv:1208.2540 [gr-qc]
[262] *A.V. Astashenok, E. Elizalde, S.D. Odintsov, and A.V. Yurov, European Physical Journal C,
to appear (2012). arXiv:1206.2192 [gr-qc]
[263] *E. Elizalde, A.N.Makarenko, S. Nojiri, V.V. Obukhov, and S.D. Odintsov, Astrophysics and
Space Science, to appear (2012). arXiv:1206.2702 [gr-qc]
[264] E. Elizalde, E.O. Pozdeeva, and S.Yu. Vernov, Classical and Quantum Gravity 30, 035002
(2013). arXiv:1209.5957 [astro-ph.CO]
[265] *A.I.Volokitin and B.N.J.Persson, Physical ReviewLetters, 106, 094502 (2011).
[266] *A.I.Volokitin and B.N.J.Persson, Physical Review B, 83, 241407 (2011) (Rapid
Communication).
[267] *A.I.Volokitin and B.N.J.Persson, New Journal of Physics, 13 (2011) 068001
[268] *A.I.Volokitin and B.N.J.Persson, Journal of Physics: Conference Series 291, 012018 (2011).
[269] *A.I.Volokitin and B.N.J.Persson, arXiv: 1302.1188 (2013)
[270] L.P. Pitaevskii, Int. J. Quantum Chem. Vol. 112, p. 2998 (2012).
[271] L.P. Pitaevskii, In: Casimir Physics, Lecture Notes in Physics, Vol. 834, pp. 23-37, Eds.
D.A.R.Dalvit, P.W. Milonni, D.C. Roberts, and F.S.S. Rosa (Springer-Verlag, Heidelberg, 2011)
[272] * L. Rizzuto, S. Spagnolo, Phys. Scr. T143, 014021 (2011)
42
[273] * R. Passante, L. Rizzuto, S. Spagnolo, S. Tanaka, T.Y. Petrosky, Phys. Rev. A 85, 062109
(2012)
[274] * N. Bartolo, R. Passante, Phys. Rev. A 86, 012122 (2012)
[275] * R. Passante, L. Rizzuto, S. Spagnolo, Eur. Phys. J. C 73, 2419 (2013)
[276] * S. Butera, R. Passante, submitted to Phys. Rev. Lett. 11(6): 060403 (2013)
[277] *G. Torricelli, P. J. van Zwol, O. Shpak, G. Palasantzas, V. B. Svetovoy, C. Binns, B. J.
Kooi, P. Jost, and M. Wuttig, Advanced Functional Materials 22, 3729 (2012).
[278] *. W. Broer, G. Palasantzas, J. Knoester, and V. B. Svetovoy, Physical Review B 85, 155410
(2012).
[279] *. V. B. Svetovoy, P. J. van Zwol, and J. Chevrier, Physical Review B 85, 155418 (2012).
[280] *V. B. Svetovoy, Z. Moktadir, M. Elwenspoek, H. Mizuta, Europhysics Letters 96, 14006
(2011).
[281] *W. Broer, G. Palasantzas, J. Knoester, and V. B. Svetovoy, Europhysics Letters 95, 30001
(2011).
[282] *O. Shpak and G. Palasantzas, PHYSICAL REVIEW A 84, 044501 (2011).
[283] *Wijnand Broer, George Palasantzas, and Jasper Knoester, Vitaly B. Svetovoy, PHYSICAL
REVIEW B 87, 125413 (2013)
[284] C. Eberlein and R. Zietal, Physical Review A 83 (2011) 052514
[285] C. Eberlein and R. Zietal, Physical Review A 86 (2012) 022111
[286] C. Eberlein and R. Zietal, Physical Review A 86 (2012) 052522
[287] R. Bennett and C. Eberlein, New Journal of Physics 14 (2012) 123035
[289] R. Bennett and C. Eberlein, Physical Review A 86 (2012) 062505
[290] C. Eberlein and R. Zietal, Physical Review A 86 (2012) 062507
[291] E. Megias, E. Ruiz Arriola, L.L. Salcedo, Physical Review Letter 109 (2012) 151601,
arXiv:1204.2424
[292] *F.J. Moral-Gamez, L.L. Salcedo, Physical Review D85 (2012) 045019, arXiv:1110.6300
[293] L.L. Salcedo, Physics Letters B700 (2011) 331-335, arXiv:1102.2400.
[294] G. L. Klimchitskaya, M. Bordag, E. Fischbach, D. E. Krause, and V. M. Mostepanenko,
International Journal of Modern Physics A, vol. 26, no. 22, pp. 3918–3929 (2011).
[295] *J. M. Munoz-Castaneda and M. Bordag, Journal of Physics A: Mathematical and
Theoretical, vol. 44, no. 41, p. 415401 (2011).
[296] L. Teo, M. Bordag, and V. Nikolaev, Physical Review D, vol. 84, no. 12, p. 125037 (2011).
[297] M. Bordag, G. Klimchitskaya, and V. Mostepanenko, Physical Review B, vol. 86, no. 16, pp.
1–14, (2012)
[298] *M. Bordag and J. M. Muñoz-Castañeda, vol. 45, no. 37, p. 374012 (2012).
[299] G. L. Klimchitskaya, M. Bordag, and V. M. Mostepanenko, International Journal of Modern
Physics A, vol. 27, no. 15, p. 1260012 (2012).
[300] M. Bordag, G. Klimchitskaya, and V. Mostepanenko, Physical Review Letters, vol. 109, no.
19, p. 199701 (2012).
[301] *M. Bordag, Physical Review D, vol. 85, no. 2, p. 025005 (2012).
Braggio, C., Carugno, G., Della Valle, F., Galeazzi, G., Lombardi, A., Ruoso, G., Zanello, D., New
Journal of Physics, 15, art. no. 013044 (2013)
[302] * Agnesi, A., Braggio, C., Carugno, G., Valle, F.D., Galeazzi, G., Messineo, G., Pirzio, F.,
Reali, G., Ruoso, G., Review of Scientific Instruments, 82 (11), art. no. 115107 (2011).
[303] Giunchi, G., Albisetti, A.F., Braggio, C., Carugno, G., Messineo, G., Ruoso, G., Galeazzi, G.,
Della Valle, F., 21 (3 PART 1), art. no. 5680940, pp. 745-747 (2011).
[304] Thomas Juffmann, Adriana Milic, Michael Müllneritsch, Peter Asenbaum, Alexander
Tsukernik, Jens Tüxen, Marcel Mayor, Ori Cheshnovsky & Markus Arndt, Nature Nanotechnology,
7, 297–300 (2012)
[305] News & Views by Zhao & Schöllkopf, Nature Nanotechnoloy 2012, Cover on the May issue
of Nature Nanotechnology 2012 (Featured as a pro-physik highlight of 2012).
43
[306] *Mojtaba Nasiri, MirFaez Miri, and Ramin Golestanian, APPLIED PHYSICS LETTERS
100, 114105 (2012)
[307] Mohammad F. Maghrebi, Ramin Golestanian, and Mehran Kardar, PHYSICAL REVIEW D
87, 025016 (2013)
[308] A. Allocca, G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Huebner,E. Il'ichev, F. Tafuri,
Journal of Superconductivity and Novel Magnetism 25 (8), 2557 (2012)
[309] *Antoniadis, I., Baessler, S., Buechner, M., Fedorov, V. V., Hoedl, S., Lambrecht, A.,
Nesvizhevsky, V. V., Pignol, G., Protasov, K. V., Reynaud, S., Sobolev, Yu., COMPTES RENDUS
PHYSIQUE 12, 755-778 (2011)
[310] *Behunin, R. O., Intravaia, F., Dalvit, D. A. R., Maia Neto, P. A., Reynaud, S., PHYSICAL
REVIEW A 85, 012504 (2012)
[311] *Behunin, R. O., Zeng, Y., Dalvit, D. A. R., Reynaud, S. PHYSICAL REVIEW A 86,
052509 (2012)
[312] *Bitbol, A.-F., Canaguier-Durand, A., Lambrecht, A., Reynaud, Serge, PHYSICAL REVIEW
B 87, 045413 (2013)
[313] *Canaguier-Durand, A., Gerardin, A., Guerout, R., Maia Neto, P. A., Nesvizhevsky, V. V.,
Voronin, A. Yu., Lambrecht, A., Reynaud, S. PHYSICAL REVIEW A 83, 032508, (2011)
[314] *Canaguier-Durand, A., Ingold, G.-L., Jaekel, M.-T., Lambrecht, A., Maia Neto, P. A.,
Reynaud, S. PHYSICAL REVIEW A 85, 052501 (2012)
*Canaguier-Durand, A., Maia Neto, P. A., Lambrecht, A., Reynaud, S. PHYSICAL REVIEW A 83,
039905 (2011)
[315] *Dufour, G., Gerardin, A., Guerout, R., Lambrecht, A., Nesvizhevsky, V. V., Reynaud, S.,
Voronin, A. Yu. PHYSICAL REVIEW A 87, 012901 (2013)
[316] *Guerout, R., Lussange, J., Rosa, F. S. S., Hugonin, J-P, Dalvit, D. A. R., Greffet, J-J,
Lambrecht, A., Reynaud, S, PHYSICAL REVIEW B 85, 180301 (2012)
[317] *Lambrecht, A., Reynaud, S., INTERNATIONAL JOURNAL OF MODERN PHYSICS A
27, pp (2012)
[318] *Lussange, J., Guerout, R., Lambrecht, A., PHYSICAL REVIEW A 86, 062502 (2012)
[319] *Lussange, J., Guerout, R., Rosa, F. S. S., Greffet, J. -J., Lambrecht, A., Reynaud, S.,
PHYSICAL REVIEW B 86, 085432 (2012)
[320] *Maia Neto, P. A., Lambrecht, A., Reynaud, S., PHYSICAL REVIEW A 86, 059901 (2012)
[322] *Maia Neto, P. A., Lambrecht, A., Reynaud, S., EPL 100, (2012)
[323] *Nesvizhevsky, V. V., Voronin, A. Yu, Lambrecht, A., Reynaud, S., NEW JOURNAL OF
PHYSICS 14, 093053 (2012)
[324] *Torricelli, G., Pirozhenko, I., Thornton, S., Lambrecht, A., Binns, C., EPL 93, 51001 (2011)
[325] *Voronin, A. Yu, Nesvizhevsky, V. V., Reynaud, S., JOURNAL OF PHYSICS B 45, 165007
(2012)
[326] *Voronin, A. Yu, Nesvizhevsky, V. V., Reynaud, S., PHYSICAL REVIEW A 85, 014902
(2012)
[327] *Dufour, G. Guerout, R., Lambrecht, A., Nesvizhevsky, V. V. Reynaud, S. Voronin, A. Yu.,
PHYSICAL REVIEW A 87, 022506 (2013)
[328] *W. Broer, G. Palasantzas, J. Knoester, V.B. Svetovoy, Phys. Rev. B 87, 125413 (2013)
[329] I. Brevik, In ”Cosmology, Quantum Vacuum, and Zeta Functions”. Edited by Sergey D.
Odintsov, Diego Saez-Gomez, and Sebastian Xambo-Descamps, pp 57-66. Springer Proceedings in
Physics No 137 (Springer, 2011).
[330] K. A. Milton, J. Wagner, P. Parashar, I. Cavero-Pelez, I. Brevik and S. ˚A. Ellingsen, In
”Cosmology, Quantum Vacuum, and Zeta Functions”. Edited by Sergey D. Odintsov, Diego Saez-
Gomez, and Sebastian Xambo-Descamps, pp 99-113. Springer Proceedings in Physics No 137
(Springer, 2011).