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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)
David Blaschke Advanced Quantum Mechanics
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
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
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
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
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
http://theory.gsi.de/Vir-Institute/http://thsun1.jinr.ru/∼dm2006/
David Blaschke Advanced Quantum Mechanics
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
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