Field Theory of Non-Equilibrium Systems

513 Pages·2023·9.227 MB·English

by  Alex Kamenev

FIELD THEORY OF NON-EQUILIBRIUM SYSTEMS
The physics of non-equilibrium many-body systems is a rapidly expanding area
of theoretical physics. Traditionally employed in laser physics and supercon-
ducting kinetics, these techniques have more recently found applications in the
dynamics of cold atomic gases, mesoscopic, and nano-mechanical systems, and
quantum computation. This book provides a detailed presentation of modern
non-equilibrium field-theoretical methods, applied to examples ranging from bio-
physics to the kinetics of superfluids and superconductors. A highly pedagogical
and self-contained approach is adopted within the text, making it ideal as a
referenceforgraduatestudentsandresearchersincondensedmatterphysics.
In this second edition, the text has been substantially updated to include recent
developments in the field such as driven-dissipative quantum systems, kinetics of
fermionswithBerrycurvature,andFloquetkineticsofperiodicallydrivensystems,
among many other important new topics. Problems have been added through-
out, structured as compact guided research projects that encourage independent
exploration.
ALEX KAMENEV is a Professor at the William I. Fine Theoretical Physics
Institute (FTPI) and at the School of Physics and Astronomy, University of Min-
nesota. His main areas of research include mesoscopic physics, low-dimensional
and correlated fermionic and bosonic models, topological systems, and quantum
computing.HeisaFellowoftheAmericanPhysicalSociety.
Published online by Cambridge University Press
Published online by Cambridge University Press
FIELD THEORY OF
NON-EQUILIBRIUM SYSTEMS
SecondEdition
ALEX KAMENEV
UniversityofMinnesota
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DOI:10.1017/9781108769266
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Contents
PrefacetotheSecondEdition pagexv
PrefacetotheFirstEdition xvi
1 Introduction 1
1.1 ClosedTimeContour 1
1.2 BriefOutlineoftheBook 6
PartI SystemswithFewDegreesofFreedom
2 Bosons 11
2.1 BosonicCoherentStates 11
2.2 PartitionFunction 13
2.3 BosonicGaussianIntegrals 15
2.4 NormalizationandContinuumNotation 16
2.5 GreenFunctions 18
2.6 KeldyshRotation 20
2.7 KeldyshActionandItsStructure 23
2.8 NonlinearInteractions 25
2.9 ExternalSources 27
2.10 Problems 31
2.10.1 UncertaintyPrinciple 31
2.10.2 BogoliubovTransformation 32
2.10.3 KeldyshPerturbationTheory 32
3 Single-ParticleQuantumMechanics 33
3.1 HarmonicOscillator 33
3.2 QuantumParticleinContactwithanEnvironment 36
3.3 FromMatsubaratoKeldysh 38
vii
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viii Contents
3.4 QuantumTunnelinginaTime-DependentPotential 39
3.5 DissipativeQuantumTunneling 43
3.6 Problems 47
3.6.1 Feynman–Keldysh Action for Symmetric
Potentials 47
3.6.2 KorshunovInstantons 47
4 ClassicalStochasticSystems 50
4.1 ClassicalDissipativeAction 50
4.2 LangevinEquation 51
4.3 MultiplicativeNoiseandMartin–Siggia–RoseMethod 52
4.4 OptimalPathApproximation 55
4.5 Fokker–PlanckEquation 59
4.6 ItoversusStratonovich 63
4.7 NoisewithaFiniteCorrelationTime 65
4.8 KramersProblem 66
4.9 Counting Statistics: Donsker–Varadhan Theory and
Beyond 68
4.10 FluctuationRelation 72
4.11 ReactionModels 75
4.12 Time-DependentProblems 79
4.13 LargeDeviationsinMultivariableSystems 82
4.14 Problems 85
4.14.1 Noise-InducedStabilization 85
4.14.2 AnomalousCountingStatistics 85
4.14.3 Lotka–VolterraModel 85
5 Driven-DissipativeSystems 87
5.1 Rotating-WaveApproximation 87
5.2 LindbladEquation 90
5.3 FromKeldyshtoLindblad 92
5.4 LinearSystems 96
5.5 QuantumHeating 100
5.6 QuantumActivation 103
5.7 DarkSpace 109
5.8 SymmetriesofDissipativeEvolution 112
5.9 LindbladianInstantons 115
5.10 OptomechanicalCooling 118
5.11 Problems 120
5.11.1 MasterEquationintheNumberBasis 120
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Contents ix
5.11.2 HusimiFunction 121
5.11.3 KineticEquation 121
5.11.4 BlochEquations 122
PartII BosonicandClassicalFields
6 BosonicFields 125
6.1 ComplexBosonicFields 125
6.2 Interactions 127
6.3 DysonEquation 129
6.4 RealBosonicFields 132
6.5 Self-Energy 135
6.6 WignerTransformation 136
6.7 KineticTerm 138
6.8 CollisionIntegral 141
6.9 Problems 145
6.9.1 DiffusioninEnergySpace 145
7 DynamicsofCollisionlessPlasma 146
7.1 PlasmaAction 146
7.2 PlasmonsandLandauDamping 149
7.3 AcousticModesinPlasma 151
7.4 RandomPhaseApproximation 153
7.5 BeyondLinearizedDynamics 157
7.6 NonlinearLandauDamping 161
7.7 Problems 163
7.7.1 LandauDampingoftheIonAcousticMode 163
8 KineticsofBoseCondensates 164
8.1 Gross–PitaevskiiEquation 164
8.2 Quasiparticles 167
8.3 CollisionlessRelaxationoftheCondensateFluctuations 172
8.4 CondensateGrowthandCollapse 175
8.5 Fluctuations 179
8.6 SemiclassicalDynamicsoftheCondensate 184
8.7 QuasiparticleCollisionIntegral 186
8.8 DynamicsofaQuantumImpurityinaSuperfluid 190
8.9 Problems 194
8.9.1 CondensateinaHarmonicTrap 194
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