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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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
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
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)
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
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
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
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
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
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
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
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