Field Theory Of Non-equilibrium Systems

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Cover Title Copyright Contents Preface to the Second Edition Preface to the First Edition 1 Introduction 1.1 Closed Time Contour 1.2 Brief Outline of the Book Part I Systems with Few Degrees of Freedom 2 Bosons 2.1 Bosonic Coherent States 2.2 Partition Function 2.3 Bosonic Gaussian Integrals 2.4 Normalization and Continuum Notation 2.5 Green Functions 2.6 Keldysh Rotation 2.7 Keldysh Action and Its Structure 2.8 Nonlinear Interactions 2.9 External Sources 2.10 Problems 2.10.1 Uncertainty Principle 2.10.2 Bogoliubov Transformation 2.10.3 Keldysh Perturbation Theory 3 Single-Particle Quantum Mechanics 3.1 Harmonic Oscillator 3.2 Quantum Particle in Contact with an Environment 3.3 From Matsubara to Keldysh 3.4 Quantum Tunneling in a Time-Dependent Potential 3.5 Dissipative Quantum Tunneling 3.6 Problems 3.6.1 Feynman￢ﾀﾓKeldysh Action for Symmetric Potentials 3.6.2 Korshunov Instantons 4 Classical Stochastic Systems 4.1 Classical Dissipative Action 4.2 Langevin Equation 4.3 Multiplicative Noise and Martin￢ﾀﾓSiggia￢ﾀﾓRose Method 4.4 Optimal Path Approximation 4.5 Fokker￢ﾀﾓPlanck Equation 4.6 Ito versus Stratonovich 4.7 Noise with a Finite Correlation Time 4.8 Kramers Problem 4.9 Counting Statistics: Donsker￢ﾀﾓVaradhan Theory and Beyond 4.10 Fluctuation Relation 4.11 Reaction Models 4.12 Time-Dependent Problems 4.13 Large Deviations in Multivariable Systems 4.14 Problems 4.14.1 Noise-Induced Stabilization 4.14.2 Anomalous Counting Statistics 4.14.3 Lotka￢ﾀﾓVolterra Model 5 Driven-Dissipative Systems 5.1 Rotating-Wave Approximation 5.2 Lindblad Equation 5.3 From Keldysh to Lindblad 5.4 Linear Systems 5.5 Quantum Heating 5.6 Quantum Activation 5.7 Dark Space 5.8 Symmetries of Dissipative Evolution 5.9 Lindbladian Instantons 5.10 Optomechanical Cooling 5.11 Problems 5.11.1 Master Equation in the Number Basis 5.11.2 Husimi Function 5.11.3 Kinetic Equation 5.11.4 Bloch Equations Part II Bosonic and Classical Fields 6 Bosonic Fields 6.1 Complex Bosonic Fields 6.2 Interactions 6.3 Dyson Equation 6.4 Real Bosonic Fields 6.5 Self-Energy 6.6 Wigner Transformation 6.7 Kinetic Term 6.8 Collision Integral 6.9 Problems 6.9.1 Diffusion in Energy Space 7 Dynamics of Collisionless Plasma 7.1 Plasma Action 7.2 Plasmons and Landau Damping 7.3 Acoustic Modes in Plasma 7.4 Random Phase Approximation 7.5 Beyond Linearized Dynamics 7.6 Nonlinear Landau Damping 7.7 Problems 7.7.1 Landau Damping of the Ion Acoustic Mode 8 Kinetics of Bose Condensates 8.1 Gross￢ﾀﾓPitaevskii Equation 8.2 Quasiparticles 8.3 Collisionless Relaxation of the Condensate Fluctuations 8.4 Condensate Growth and Collapse 8.5 Fluctuations 8.6 Semiclassical Dynamics of the Condensate 8.7 Quasiparticle Collision Integral 8.8 Dynamics of a Quantum Impurity in a Superfluid 8.9 Problems 8.9.1 Condensate in a Harmonic Trap 8.9.2 Collective Modes of the Condensate in the Harmonic Trap 8.9.3 Dark Solitons 8.9.4 Beliaev Damping 9 Dynamics of Phase Transitions 9.1 Dissipative Chains and Membranes 9.2 Equilibrium Statistical Mechanics 9.3 Critical Nucleation in First-Order Transitions 9.4 Dynamics Near a Classical Second-Order Transition 9.5 Hohenberg￢ﾀﾓHalperin Classification 9.6 Quantum Phase Transitions 9.7 Absorbing State Transitions 9.8 KPZ Dynamics of Growing Interfaces 9.9 Large Deviations in Stochastic Systems 9.10 Problems 9.10.1 Edwards￢ﾀﾓWilkinson Universality Class 9.10.2 Height Distribution in 1d Edwards￢ﾀﾓWilkinson Model 9.10.3 Soliton Solutions of Large Deviation Equations Part III Fermions 10 Fermions 10.1 Grassmann Variables and Integrals 10.2 Partition Function 10.3 Green Functions and Keldysh Rotation 10.4 Free Fermionic Fields and Their Action 10.5 External Fields and Sources 10.6 Free Degenerate Fermi Gas 10.7 Interactions 10.8 Stoner Instability 10.9 Problems 10.9.1 Fermionic Bogoliubov Transformation 10.9.2 Random Matrices via Fermionic Replica 10.9.3 Fermionic Lindbladian Action 11 Kinetic Theory and Hydrodynamics 11.1 Kinetic Equation 11.2 Hydrodynamics of the Fermi Liquid 11.3 Hydrodynamic Modes 11.4 Magnetization Dynamics 11.5 Problems 11.5.1 H-Theorem 11.5.2 Hydrodynamics of Electron Flow 12 Aspects of Kinetic Theory 12.1 Kinetic Equation in Presence of the Berry Curvature 12.2 Floquet Kinetic Theory 12.3 Kinetic Equation as a Stationary Point of the O G- O6 Action 12.4 Boltzmann￢ﾀﾓLangevin Kinetic Equation 12.5 The Butterfly Effect and OTOC 12.6 Problems 12.6.1 Linearized Kinetic Equation 12.6.2 Near-Field Heat Transfer 13 Quantum Transport 13.1 Landauer Formula 13.2 Shot Noise 13.3 Counting Statistics 13.4 Fluctuation Relation 13.5 Adiabatic Pumping 13.6 Spin Torque 13.7 Problems 13.7.1 Meir￢ﾀﾓWingreen Formula 13.7.2 Levitons: Optimal Voltage Pulses Part IV Disordered Metals and Superconductors 14 Disordered Fermionic Systems 14.1 Kinetic Equation Approach 14.2 Averaging over the Quenched Disorder 14.3 Nonlinear Sigma-Model 14.4 Stationary Point and Fluctuations 14.5 Sources and External Fields 14.6 Kubo Formula and Linear Response 14.7 Cooper Channel 14.8 Weak Localization and Scaling 14.9 Time-Dependent Perturbations 14.10 Problems 14.10.1 Temperature Profile in a Mesoscopic Wire 14.10.2 Electrodynamics of Disordered Metals 14.10.3Weak Localization Magneto-Conductance 15 Mesoscopic Effects 15.1 Spectral Statistics 15.2 Wigner￢ﾀﾓDyson Statistics 15.3 Universal Conductance Fluctuations 15.4 Full Counting Statistics in a Disordered Wire 15.5 Tunneling Action 15.6 Chaotic Cavity 15.7 Problems 15.7.1 Aharonov￢ﾀﾓBohm Conductance Oscillations 16 Electron￢ﾀﾓElectron Interactions in Disordered Metals 16.1 K-Gauge 16.2 Nonlinear Sigma-Model for Interacting Systems 16.3 Zero Bias Anomaly 16.4 Altshuler￢ﾀﾓAronov Effect 16.5 Kinetic Equation 16.6 Problems 16.6.1 Semiclassical Treatment of the Zero Bias Anomaly 16.6.2 Near-Field Heat Transfer in Disordered Metals 17 Dynamics of Disordered Superconductors 17.1 Cooper Channel Interactions 17.2 Usadel Equation 17.3 Stationary Superconductivity 17.4 SNS System 17.5 Collective Modes of Disordered Superconductors 17.6 Time-Dependent Ginzburg￢ﾀﾓLandau Theory 17.7 Fluctuating Superconductivity 17.8 Problems 17.8.1 Gapless Superconductivity 17.8.2 Microwave Absorption in Superconductors 17.8.3 Stimulated Superconductivity 18 Electron￢ﾀﾓPhonon Interactions 18.1 Phonon Action and Propagators 18.2 Frￃﾶhlich and Pippard Electron￢ﾀﾓPhonon Interactions 18.3 Nonlinear Sigma￢ﾀﾓModel for Electron￢ﾀﾓPhonon Interactions 18.4 Electron Kinetics in Normal Metals 18.5 Kinetics of Quasiparticles in Superconductors 18.6 Phonon Kinetics 18.7 Ultrasound Attenuation 18.8 Problems 18.8.1 Temperature Profile in a Conductor 18.8.2 Phonon Diffusion 18.8.3 Quantum Correction to Electron￢ﾀﾓPhonon Vertex 18.8.4 Sigma-Model with Moving Impurities References Index