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Advanced Quantum Mechanics David Blaschke Introduction Symmetry Breaking Temperature Density Strong Fields Particle Production Schwinger Kinetics Applications Lasers Astrophysics Perspectives Projects Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics University of Wroclaw, Poland Bogoliubov Laboratory for Theoretical Physics Joint Institute for Nuclear Research Dubna, Russia Lectures for PhD students, Winter Semester 2006/2007 David Blaschke Advanced Quantum Mechanics

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Page 1: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Advanced Quantum MechanicsMacroscopic Quantum Effects: from Laboratory to Stars

David Blaschke

Institute for Theoretical PhysicsUniversity of Wroclaw, Poland

Bogoliubov Laboratory for Theoretical PhysicsJoint Institute for Nuclear Research Dubna, Russia

Lectures for PhD students, Winter Semester 2006/2007

David Blaschke Advanced Quantum Mechanics

Page 2: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

1 Introduction2 Symmetry Breaking and Restoration

High TemperaturesHigh DensitiesStrong Fields

3 Problem: Particle ProductionSchwinger mechanismKinetic equation for particle production

4 ApplicationsOptical and X-ray Laser ExperimentsCompact Astrophysical Objects

5 Perspectives6 Projects

David Blaschke Advanced Quantum Mechanics

Page 3: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Introduction to scientific background

Academic tradition

Bogoliubov

ShirkovZubarev

RopkeSmolyanskyTavkhelidze

JINR-2004 8

JINR

Dubna

DDuubbnnaa

JJIINNRR

FoundersFounders

V.P.Dzhelepov

M.G.Meshcheryakov

V.I.VekslerN.N.Bogoliubov, D.I.Blokhintsev

G.N.FlerovI.M.Frank

B. Pontecorvo

H.Niewodniczanski

L.Infeld Wang GanchangG.Najakov

TextbooksBogoliubov/ Shirkov: Quantum Field Theory (1959)

Zubarev/Morozov/Ropke: Statistical Mechanics of NonequilibriumProcesses (1996)

David Blaschke Advanced Quantum Mechanics

Page 4: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Symmetry Breaking and Restoration

High Temperature

Deconfinement at Tc ∼ TH

Strongly interacting QGP inHeavy ion collisions

Signal: J/ψ suppression

CERN − NA50 Data vs. Theory

� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �

� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �

SimulationsLattice QCD

NUCLOTRON

Mott−Hagedorn Gas

Lattice QCD Data vs.

QCD Equation of State

Blaschke, Bugaev: Prog. Part. Nucl. Phys. 53 (2004) 197

David Blaschke Advanced Quantum Mechanics

Page 5: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Symmetry Breaking and Restoratoion

High Densities

Quark matter phases at3-5 nuclear densities

Color superconductivity

Interiors of Compact Stars

Cooling of Compact Stars

10 12R [km]

0.5

1

1.5

2

M [M

sol]

typi

cal s

tars

Nstarhybrid

2 3 4 5 6log10(t[yr])

5

5,2

5,4

5,6

5,8

6

6,2

6,4

log 10

(Ts [K

])

Model IVCrab

3C58Vela

RX

J18

56

hybr

id s

tars

1.051.131.22 (critical)1.281.351.451.551.651.75

350 400 450 500 550

Chemical Potential µ [MeV]

0

10

20

30

40

50

60

70

80

Tem

per

atu

re

T [

MeV

]

g2SC

175

NQ-2SC CFL

0.90.8

gCFL

guSC

2SC

χ2SC = 1.0

0.7

NQ

Ms=2

00 M

eV

Blaschke, Grigorian, Voskresensky: Phys. Rev. C71 (2005) 045801

David Blaschke Advanced Quantum Mechanics

Page 6: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

New: Pair Creation in Strong Fields

Heavy Ion Collisions

Magnetars: B∼ 1015G

Optical and X-Ray Lasers:E∼ 1015 ÷ 1017 V/m

Extreme Light Infrastructure (Project)

� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �

Artist view of a Magnetar (NASA)

David Blaschke Advanced Quantum Mechanics

Page 7: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Schwinger mechanism for pair production

Pair creation as quantum tunneling

2εT

2 εT

/E2 ε T

xEpositive levels

negative levelsnegative levels

positive levels

Schwinger result for pair production rate

dN

d3xdt=

(eE)2

4π3

∞Xn=1

1

n2exp

„−nπ

Ecrit

E

«

J. Schwinger: On Gauge Invariance and VacuumPolarization, Phys. Rev. 82 (1951) 664

To ’materialize’ a virtual e+e− pair in a constantelectric field E the separation d must be sufficientlylarge

eEd = 2mc2

Probability for separation d as quantum fluctuation

P ∝ exp

„−

d

λc

«= exp

2m2c3

e~E

!

= exp

„−

2Ecrit

E

«

Emission sufficient for observation when E ∼ Ecrit

Ecrit ≡m2c3

e~' 1.3× 1018

V/m

For time-dependent fields: Kinetic Equation approachfrom Quantum Field Theory

David Blaschke Advanced Quantum Mechanics

Page 8: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Kinetic fromulation of pair production

Kinetic equation for the distribution function f (P, t) = 〈0|a+P(t)aP(t)|0〉

−3 −2 −1 0 1 2 3 4 5τ

0

1

2

3

4

5

f −(τ)

/exp

(−π/

E0)

E0 = 0.7E0 = 1.0E0 = 1.5E0 = 3.0

Schwinger limit (constant field) reproduced

f (τ →∞) = exp

„−π

E0

«

Schmidt, Blaschke, Smolyansky et al:Non-Markovian effects in strong-field pair creation,Phys. Rev. D 59 (1999) 094005

df±(p, t)

dt=

∂f±(p, t)

∂t+ eE(t)

∂f±(p, t)

∂p‖(t)

=eE(t)ε⊥

2ω2(t)

Z t

−∞dt′

eE(t′)ε⊥

ω2(t′)

× [1± 2f±(p, t′)]cosˆ Z t

t′dτω(τ)

˜Kinematic momentum p = (p1, p2, p3 − eA(t)),

Time-dependent Bogoliubov-transformation

ap(t) = αp(t)ap(t0) + βp(t)b+−p(t0)

bp(t) = α−p(t)bp(t0)− β−p(t)a+−p(t0)

Anti-commutating field operators

{ap(t0), a+p′ (t0)} = {bp(t0), b+

p′ (t0)} = δp,p′

David Blaschke Advanced Quantum Mechanics

Page 9: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Laser Experiments: Jena Multi-TW Laser

Colliding laser pulses of a Ti:sapphire laser with

Em/Ecrit ≈ 1.5 · 10−6 and ν/m = 2.84 · 10−6

Laser diagnostic by nonlinear Thomson scattering off

e− in a He-gas jetPulse intensity: I = 1018 W/cm2,duration: τL ∼ 80fs, wavelength: λ = 700 nm,

cross-size: z0 = 9µm

Heinzl, Sauerbrey, Schwoerer, et al, arXiv:hep-ph/0601076 (2006)

David Blaschke Advanced Quantum Mechanics

Page 10: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Laser Experiments: Jena Multi-TW Laser

Analytic estimate for Em � Ecrit, f � 1

n(t) =1

2(2π)3

Zdp (m2 + p2

⊥)

×

˛˛ tZt0

dt1eE(t1)

ε2(t1)exp

0B@2i

tZt1

dt2ε(t2)

1CA˛˛

2

Mean pair density (low frequency limit ν � m)

〈n〉 ≈ 1.6× 10−3 (eE)2

m=

„m

ν

«2nr

Observable signal: two-photon annihilation!

e+

e−p1

2p

γ

γ

Number of e+e− pairs in the volume λ3 for aweak field (Jena Ti:AlO3 laser, solid line) andfor near-critical field Em/Ecrit = 0.24,λ = 0.15 nm (X-FEL, dashed line).

Jena Experiment currentlyperformed

Prediction:

5-10 gamma-pairs per laser pulse !

Blaschke, Prozorkevich, Roberts, Schmidt, Smolyansky: PRL 96, 140402 (2006).

David Blaschke Advanced Quantum Mechanics

Page 11: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Compact stars: X-ray bursts

A low-mass X-ray binary system

David Blaschke Advanced Quantum Mechanics

Page 12: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Compact stars: X-ray bursts

RXTE observes burstspectra of EXO 0748-676with redshifted Fe-lines

Quark matter core is notexcluded.

13

Observation of redshiftz=0.35 puts constraintson compactness M/R, i.e.on neutron star EoS

Grigorian, Blaschke, Aguilera,

Phys. Rev. C 69 (2004) 065802

New constraints to EoST. Klahn et al: nucl-th/0602038

David Blaschke Advanced Quantum Mechanics

Page 13: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Gamma-Ray Bursts: Magnetars or Black holes?

GRB’s as new ’standardcandles’ to measure thespace-time structure ofthe UniverseGhirlanda et al: ApJ 613, L13 (2004)

Understanding GRB’s is achallenge to QFT underextreme conditions!

Relation to kinetic theoryof pair production instrong fieldsRuffini et al: astro-ph/0410233 (2004)

INTEGRAL and SWIFTmissions observe GRB’s

David Blaschke Advanced Quantum Mechanics

Page 14: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Perspectives

VH−VI−041

Dense Hadronic Matter and QCD Phase TransitionVirtual Institute of the Helmholtz−Association

http://theory.gsi.de/Vir-Institute/http://thsun1.jinr.ru/∼dm2006/

David Blaschke Advanced Quantum Mechanics

Page 15: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Perspectives

http://luth.obspm.fr/%7ecarter/CompStar/

Physics of Compact Stars

L. Rezzolla (Postdam), S. Rosswog (Bremen)

M. Liebendoerfer (Basel), J. Pons (Alicante)

Proposal for a 6−week Ph.D. training programmeECT* Trento, Italy

September 3 − October 12, 2007

Organizers: D. Blaschke (Wroclaw), J. Pons (Alicante), L. Rezzolla (Potsdam)

P. Haensel (Warsaw), P. Pizzochero (Milan)* EoS for Compct Star Interiors:

* Computational Relativistic Astrophysics:

* Supernovae and Protoneutron Stars:

D. Voskresensky (Moscow), D. Page (Mexico)

F. Burgio (Catania), D. Blaschke (Wroclaw)

D. Jones (Southampton), R. Turolla (Padova)* Compact Star Phenomenology:

* Physics of the Neutron Star Crust:

* Neutrino Processes and Cooling:

http://www.ect.it

David Blaschke Advanced Quantum Mechanics

Page 16: Advanced Quantum Mechanicsblaschke/vorles/AQM_0.pdf · Advanced Quantum Mechanics Macroscopic Quantum Effects: from Laboratory to Stars David Blaschke Institute for Theoretical Physics

AdvancedQuantumMechanics

DavidBlaschke

Introduction

SymmetryBreaking

Temperature

Density

Strong Fields

ParticleProduction

Schwinger

Kinetics

Applications

Lasers

Astrophysics

Perspectives

Projects

Projects

First Project:Symmetry breaking. Goldstone theorem. Higgs-effectSecond Project:Bose condensation. Superconductivity. SuperfluidityThird Project:Pair production in strong fields. Schwinger mechanismFourth Project:Hawking radiation. Unruh effectFifth Project:Confinement of Quarks and Gluons

David Blaschke Advanced Quantum Mechanics