Field Theory of Non-Equilibrium Systems

357 Pages·2011·3.07 MB·English

by  Kamenev A.

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FIELD THEORY OF NON-EQUILIBRIUM SYSTEMS
The physics of non-equilibrium many-body systems is one of the most rapidly
expanding areas of theoretical physics. Traditionally used in the study of laser
physics and superconducting kinetics, these techniques have more recently found
applications in the study of dynamics of cold atomic gases, mesoscopic and
nano-mechanicalsystems.
Thebookgivesaself-containedpresentationofthemodernfunctionalapproach
tonon-equilibriumfield-theoreticalmethods.Theyareappliedtoexamplesranging
frombiophysicstothekineticsofsuperfluidsandsuperconductors.Itsstep-by-step
treatment gives particular emphasis to the pedagogical aspects, making it ideal as
a reference for advanced graduate students and researchers in condensed matter
physics.
ALEX KAMENEV is a Professor of Theoretical Condensed Matter Physics at
the William I. Fine Theoretical Physics Institute (FTPI) and in the Department
of Physics, University of Minnesota. Since gaining his Ph.D. at the Weizmann
Institute of Science in 1996, he has held a postdoctoral position at the University
ofCaliforniaatSantaBarbaraandanAssistantProfessorshipattheIsraelInstitute
ofTechnology(Technion).Hismainareasofresearchincludemesoscopicphysics,
low-dimensionalandcorrelatedfermionicandbosonicmodelsaswellasstochastic
systemsandpopulationdynamics.

FIELD THEORY OF
NON-EQUILIBRIUM SYSTEMS
ALEX KAMENEV
CAMBRIDGE UNIVERSITY PRESS
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(cid:2)c A.Kamenev2011
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Firstpublished2011
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
Kamenev,Alex,1964–
Fieldtheoryofnon-equilibriumsystems/AlexKamenev.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-521-76082-9
1. Quantumfieldtheory. 2. Condensefmatter. I. Title.
QC174.45.K36 2011
(cid:3)
530.143–dc23
2011023917
ISBN978-0-521-76082-9Hardback
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ToInna,Iris,AlisaandMark

Contents
Preface pagexi
1 Introduction 1
1.1 Closedtimecontour 1
1.2 Theoutlineofthisbook 6
2 Bosons 10
2.1 Bosoniccoherentstates 10
2.2 Partitionfunction 12
2.3 BosonicGaussianintegrals 14
2.4 Normalizationandcontinuumnotation 15
2.5 Greenfunctions 17
2.6 Keldyshrotation 19
2.7 Keldyshactionanditsstructure 22
2.8 Externalsources 24
3 Single-particlequantummechanics 29
3.1 Harmonicoscillator 29
3.2 Quantumparticleincontactwithanenvironment 32
3.3 FromMatsubaratoKeldysh 34
3.4 Quantumtunnelinginatime-dependentpotential 36
3.5 Dissipativequantumtunneling 39
4 Classicalstochasticsystems 44
4.1 Classicaldissipativeaction 44
4.2 Langevinequation 45
4.3 MultiplicativenoiseandMartin–Siggia–Rosemethod 46
4.4 Optimalpathapproximation 49
4.5 Fokker–Planckequation 53
4.6 Itovs.Stratonovich 57
4.7 Noisewithafinitecorrelationtime 59
vii
viii Contents
4.8 Kramersproblem 60
4.9 Fluctuationrelation 62
4.10 Reactionmodels 65
4.11 Time-dependentproblems 69
4.12 Largedeviationsinmultivariablesystems 72
5 Bosonicfields 76
5.1 Complexbosonicfields 76
5.2 Interactions 78
5.3 Dysonequation 80
5.4 Realbosonicfields 83
5.5 Self-energy 86
5.6 Wignertransformation 87
5.7 Kineticterm 89
5.8 Collisionintegral 92
6 Dynamicsofcollisionlessplasma 97
6.1 Plasmaaction 97
6.2 PlasmonsandLandaudamping 101
6.3 Acousticmodesinplasma 102
6.4 Randomphaseapproximation 104
6.5 Beyondlinearizeddynamics 108
6.6 Non-linearLandaudamping 112
7 KineticsofBosecondensates 115
7.1 Gross–Pitaevskiiequation 115
7.2 Quasiparticles 118
7.3 Collisionlessrelaxationofthecondensatefluctuations 123
7.4 Condensategrowthandcollapse 126
7.5 Fluctuations 131
7.6 Semiclassicaldynamicsofthecondensate 135
7.7 Quasiparticlecollisionintegral 137
7.8 Dynamicsofaquantumimpurityinasuperfluid 141
8 Dynamicsofphasetransitions 147
8.1 Dissipativechainsandmembranes 147
8.2 Equilibriumstatisticalmechanics 149
8.3 Criticalnucleationinfirstordertransitions 151
8.4 Criticaldynamicsnearaclassicalsecondordertransition 154
8.5 Hohenberg–Halperinclassification 160
8.6 Quantumphasetransitions 163
8.7 Absorbingstatetransitionsinreaction-diffusion
models 166
8.8 Dynamicsofgrowingsurfaces 176