![Page 1: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/1.jpg)
Vortices, Superfluid turbulence & Condensate Formation in Bose Gases
Thomas Gasenzer
Institut für Theoretische Physik Ruprecht-Karls Universität Heidelberg
Philosophenweg 16 • 69120 Heidelberg • Germany
email: [email protected]: www.thphys.uni-heidelberg.de/~gasenzer
![Page 2: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/2.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Thanks & credits to...
...my work group in Heidelberg:
Sebastian BockSebastian ErneMartin GärttnerRoman HennigMarkus KarlSteven MatheyBoris NowakNikolai PhilippMaximilian SchmidtJan Schole Dénes SextyMartin TrappeJan Zill
...my former students:
Cédric Bodet ( NEC), Alexander Branschädel ( KIT Karlsruhe), Stefan Keßler ( U Erlangen), Matthias Kronenwett ( R. Berger), Christian Scheppach ( Cambridge, UK), Philipp Struck ( Konstanz), Kristan Temme ( Vienna)
LGFG BaWue
€€€...
ExtreMe Matter Institute
![Page 3: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/3.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
ULTRAcool...
... atoms @ nanokelvins –
trapped only a few mm away from
glass cell @ room temperature
(vacuum of 10-12 Torr, i.e. 10-15 bar,or 10-10 Pa,
≈ atmospheric pressure on the moon)
Heavy-Ion collisions (~1015 K)
![Page 4: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/4.jpg)
Condensate formationin an ultracold Bose gas
![Page 5: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/5.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Bose-Einstein condensation
Bose-Einstein condensation (BEC)
bimodaldistribution
Experimental picture after free expansion of the trapped cloud:
dens
ity
![Page 6: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/6.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Equilibration
Transient, metastable statee.g. Turbulence
Non-thermal fixed point
![Page 7: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/7.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Superfluid hydro of Bose-condensed Gas
The Gross-Pitaevskii Equation, (g = 4πa0/m)
using defs.
can be written as
Euler equation
![Page 8: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/8.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Movie 1: Phase evolution & Spectrum
n(k) = *(k)(k)∣angle average
Movie by Jan Schole
http://www.thphys.uni-heidelberg.de/~smp/gasenzer/videos/boseqt.html
![Page 9: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/9.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Movie 2: Vortex “gas” & Spectrum
n(k) = *(k)(k)∣angle average
http://www.thphys.uni-heidelberg.de/~smp/gasenzer/videos/boseqt.html
![Page 10: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/10.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Spectrum in 2+1 DB. Nowak, D. Sexty, TG, PRB 84: 020506(R), 2011
![Page 11: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/11.jpg)
Wave turbulencein an ultracold Bose gas
![Page 12: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/12.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Wave turbulenceStationary scaling n(k) within inertial region:
log n(k)
log k
n(k) ~ k—ζ
pump
dumpcascadeCascade
![Page 13: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/13.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Dilute ultracold Bose Gas
Gross-Pitaevskii Equation: (g = 4πa0/m)
Momentum spectrum:
n(k) = *(k)(k)
![Page 14: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/14.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Bose gas in d spatial dimensions
momentum k
ζ = d
C. Scheppach, J. Berges, TG PRA 81 (10) 033611
n ζQ = d −2/3
n ~ k −ζ
J. Berges, A. Rothkopf, J. Schmidt, PRL 101 (08) 041603
![Page 15: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/15.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Bose gas in d spatial dimensions
momentum k
ζ = 2
thermalequilibrium
(Rayleigh-Jeans)
C. Scheppach, J. Berges, TG PRA 81 (10) 033611
n
n ~ k −ζ
J. Berges, A. Rothkopf, J. Schmidt, PRL 101 (08) 041603
ζ = dζ
Q = d −2/3
![Page 16: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/16.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Dyn. QFT: Resummed Vertex
p = ( p0, p):
Vertex bubble resummation:(e.g. 2PI to NLO in 1/N)
[Dynamics: J. Berges, (02); G. Aarts et al., (02);[Nonthermal fixed points: J. Berges, A. Rothkopf, J. Schmidt, PRL (08)]
![Page 17: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/17.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
momentum k
ζQ = d + 2
C. Scheppach, J. Berges, TG PRA 81 (10) 033611 J. Berges, A. Rothkopf, J. Schmidt, PRL 101 (08) 041603; J. Berges, G. Hoffmeister, NPB 813, 383 (2009)
nζ = d + 2 + z
Bose gas in d spatial dimensions n ~ k −ζ
New exponentbeyond Quantum Boltzmann!
ζ = dζ
Q = d −2/3
![Page 18: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/18.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Dyn. QFT: Resummed Vertex
p = ( p0, p):
Vertex bubble resummation:
![Page 19: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/19.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Cascades in 2+1 D
pump
pump
![Page 20: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/20.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Decomposition of Energy
![Page 21: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/21.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Time evolution of Energy Components (3+1 D)
J. Schole, B. Nowak, D. Sexty, TG (unpublished)
interaction energy
incompressible flow
quantum pressure contr.
compressible flow
vortexformation
![Page 22: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/22.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Evolution of Zero-Mode
J. Schole, B. Nowak, D. Sexty, TG (unpublished)
![Page 23: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/23.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Mode Occupations
J. Schole, B. Nowak, D. Sexty, TG (unpublished)
![Page 24: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/24.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
1st-order Coherence
J. Schole, B. Nowak, D. Sexty, TG (unpublished)
![Page 25: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/25.jpg)
Random vortex distributions
![Page 26: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/26.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Point vortex model
nk ~ k −4 nk ~ k
−2, k < kpair
nk ~ k −4, k > kpair
B. Nowak, J. Schole, D. Sexty, TG, arXiv:1111.61XX [cond-mat.quant-gas]
![Page 27: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/27.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Point vortex model in 2+1 D
paired : k-2
random distrib.: k-4
vortex core: k-6
B. Nowak, J. Schole, D. Sexty, TG, arXiv:1111.61XX [cond-mat.quant-gas]
![Page 28: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/28.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Simulations in 2+1 D
paired : k-2 random distrib.: k-4
thermal: k-2
B. Nowak, J. Schole, D. Sexty, TG, arXiv:1111.61XX [cond-mat.quant-gas]
![Page 29: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/29.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex position correlationsD
ensi
ty –
Den
sity
cor
rela
tion
s vortex-antivortex
vortex-vortex
minus
Distance between vorticesB. Nowak, J. Schole, D. Sexty, TG, arXiv:1111.61XX [cond-mat.quant-gas]
![Page 30: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/30.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Density Decay in 2d
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 31: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/31.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortices in a Na condensate
![Page 32: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/32.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Movie 3: Vortex Lines in 3+1 D
n(k) = *(k)(k)∣angle average
http://www.thphys.uni-heidelberg.de/~smp/gasenzer/videos/boseqt.html
![Page 33: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/33.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
3+1 D simulationsB. Nowak, D. Sexty, TG, PRB 84: 020506(R), 2011
![Page 34: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/34.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Line vortex model in 3+1 Dsmall circular rings: k-2
paired parallel lines: k-3
independent lines: k-5
![Page 35: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/35.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Simulations in 3+1 D
small elliptical rings: k-3
thermal: k-2
independent lines: k-5
![Page 36: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/36.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Decomposition of flow
solenoidal (incompressible) “condensate”
compressible “sound”“quantum pressure”
k-4
![Page 37: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/37.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Acoustic turbulence
compressible “sound”“quantum pressure”
solenoidal (incompressible) “condensate”
total
k-4
B. Nowak, J. Schole, D. Sexty, TG, arXiv:1111.61XX [cond-mat.quant-gas]
![Page 38: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/38.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Non-thermal fixed point
[Fig. courtesy: J. Berges '08]
![Page 39: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/39.jpg)
Relativistic scalar field
![Page 40: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/40.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Strong Turbulence
∂t2−∂ x
2x , t 3 x ,t =0
Simulations of the non-linear Klein-Gordon equation, O(2) symmetry
TG, B. Nowak, D. Sexty, arXiv:1108.0541 [hep-ph]
Initial condition: Highly occupied zero mode, Unoccupied modes with k>0
(video)
See also: http://www.thphys.uni-heidelberg.de/~sexty/videos
![Page 41: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/41.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Strong Turbulence = Charge Separation
TG, B. Nowak, D. Sexty, arXiv:1108.0541 [hep-ph]cf. also Tkachev, Kofman, Starobinsky, Linde (1998)
Modulus of complex field || vs. mean charge distribution
![Page 42: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/42.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Strong Turbulence = Charge Separation
TG, B. Nowak, D. Sexty, arXiv:1108.0541 [hep-ph]
Charge density distribution vs. power spectrum
(d = 2, N = 2)
![Page 43: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/43.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Thanks & credits to...
...my work group in Heidelberg:
Boris NowakMaximilian SchmidtJan Schole Dénes SextySebastian ErneSteven MatheyNikolai PhilippSebastian BockMartin GärttnerMartin TrappeJan ZillRoman Hennig
...my former students:
Cédric Bodet ( NEC), Alexander Branschädel ( KIT Karlsruhe), Stefan Keßler ( U Erlangen), Matthias Kronenwett ( R. Berger), Christian Scheppach ( Cambridge, UK), Philipp Struck ( Konstanz), Kristan Temme ( Vienna)
LGFG BaWue
€€€...
ExtreMe Matter Institute
![Page 44: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/44.jpg)
Supplementary slides
![Page 45: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/45.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Time-Evolution of Energy-components (2+1 D)
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 46: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/46.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Time evolution of vortex density
J. Schole, B. Nowak, D. Sexty, TG (unpublished)
![Page 47: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/47.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Enstrophy in classical turbulence
V. Yakhot, J. Wanderer, PRL 93:154502
![Page 48: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/48.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Density Decay in 2d
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 49: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/49.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Density Decay in 2d
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 50: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/50.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Kinetic Theory
One of the power laws can be explained by a kinetic theory:
∂t nv t =−ndipann
ann=coll
coll=l
v
l~ 1nv
~d
v=1d
d= 1
nv
ndip~nv
⇒ ∂ tnv t ~−nv2 ⇒ nv t ~t
−1
This result is valid under the assumption that the vortices are moving in pairsand that the pairs are homogeneously distributed.
: average pair distance
: average pair velocity
: mean free path
d
v
l
![Page 51: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/51.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Distribution
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 52: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/52.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Antivortex-Correlations
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 53: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/53.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex-Antivortex-Correlations
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 54: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/54.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Simulations in 2+1 D E(k) = ω(k)k d – 1n(k)
Remember:q
solenoidal
rotationless
k0
E(k) ~ k ‒5/3
k ‒1
B. Nowak, D. Sexty, TG (arXiv:1012.4437), PRB tbp.
![Page 55: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/55.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Simulations in 2+1 D E(k) = ω(k)k d – 1n(k)
Remember:q
solenoidal
rotationless
k0
E(k) ~ k ‒5/3
k ‒1
B. Nowak, D. Sexty, TG (arXiv:1012.4437), PRB tbp.
![Page 56: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/56.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex velocity distribution
J. Schole, B. Nowak, D. Sexty, TG (unpublished)s. also C.F. White et al., PRL 104 (10); I.A. Min, Phys. Fluids 8 (96)
Lathrop expt. [PRL 101 (08)]
![Page 57: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/57.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Velocity distributions
Paoletti et al. PRL 101, 154501 (2008):
Min et al. Phys. Fluids 8, 1169 (1996), White et al. PRL 104, 075301 (2010):
Power law tails distinguish classical turbulence from classical turbulence.
Point vortices: Power law tails
Vorticity patches: Gaussian distributions
White et al. PRL 104, 075301 (2010)
![Page 58: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/58.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Velocity distributions (Field)
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 59: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/59.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Velocity distributions (Vortices)
J. S., B. Nowak, D. Sexty, T. Gasenzer (unpublished)
![Page 60: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/60.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Condensation
N.G. Berloff, S.V. Svistunov, PRA 66, 013603 (2002)
![Page 61: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/61.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Simulations in 3+1 D
B. Nowak, D. Sexty, TG (arXiv:1012.4437)
![Page 62: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/62.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Energies
![Page 63: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/63.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Wave Turbulence – e.g. on water [H. Xia et al., EPL 91 (10) 14002]
![Page 64: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/64.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Wave Turbulence – e.g. on water [H. Xia et al., EPL 91 (10) 14002]
[Zakharov & Filonenko (67)]
Theory prediction:
![Page 65: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/65.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Vortex pairs
[T.W. Neely et al. PRL 104 (10)]
Guadeloupe [NASA]
Tucson [AZ]
![Page 66: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/66.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Helmholtz Vortex Law
[T.W. Neely et al. PRL 104 (10)]
Guadeloupe [NASA]
Tucson [AZ]
![Page 67: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/67.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
density n
phase φ
[W. P. Reinhardt, Seattle]
[Wolfgang Ketterle, MIT]
complex field
velocity
Quantum Vortices
![Page 68: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/68.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Nonlinear dynamics: Pattern formation
![Page 69: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/69.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Nonlinear dynamics: Pattern formation
![Page 70: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/70.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Thermalisation dynamics: Turbulence?
[J.
Berg
es]
• Cosmology: Reheating after Inflation••
••••••
•
![Page 71: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/71.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Turbulence in reheating after inflation
∂t2−∂ x
2x , t 3 x ,t =0
Simulations of the non-linear Klein-Gordon equation,
Kofmann, Linde, Starobinsky (96)Micha, Tkachev, PRL & PRD (04)
Initial condition: Highly occupied zero modeUnoccupied modes with k>0
Turbulent spectrum emerges
Exponent: weak wave turbulence
![Page 72: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/72.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Wave turbulence
Turbulent thermalisation after universe inflation
[Micha & Tkachev, PRL 90 (03) 121301, PRD 70 (04) 043538]
![Page 73: Vortices, Superfluid turbulence...Vortices, Superfluid turbulence & Condensate Formation in Bose Gases Thomas Gasenzer Institut für Theoretische Physik Ruprecht-Karls Universität](https://reader030.vdocuments.us/reader030/viewer/2022040319/5e45125f6ff68e55e000f52a/html5/thumbnails/73.jpg)
Heidelberg · Thermalization in Nonabelian Plasmas · 14 December 2011 Thomas Gasenzer
Lewis Fry Richardson, FRS (1881-1953)
Big whirls have little whirls that feed on their velocity,and little whirls have lesser whirls and so on to viscosity.
(L.F. Richardson, The supply of energy from and to Atmospheric Eddies, 1920)
Great fleas have little fleas upon their backs to bite 'em,And little fleas have lesser fleas, and so ad infinitum.And the great fleas themselves, in turn, have greater fleas to go on;While these again have greater still, and greater still, and so on.
(Augustus de Morgan, A Budget of Paradoxes, 1872, p. 370)
So, naturalists observe, a fleaHas smaller fleas that on him prey;And these have smaller still to bite 'em;And so proceed ad infinitum.
(Jonathan Swift: Poetry, a Rhapsody, 1733)