Keldysh technique and non-linear sigma-model: basic principles and applications

Abstract

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear sigma-model for disordered metals and superconductors. We discuss such topics as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equation, etc. The sections devoted to disordered superconductors include Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a substantial extension of arXiv:cond-mat/0412296.)

Review: 103 pages, 19 figures

References in corpus (17)

• Using a quantum dot as a high-frequency shot noise detector
• A double-dot quantum ratchet driven by an independently biased quantum point contact
• Density of states and supercurrent in diffusive SNS junctions: role of nonideal interfaces and spin-flip scattering
• Many-body theory of non-equilibrium systems
• Coulomb drag in quantum circuits
• The Keldysh action of a multi-terminal time-dependent scatterer
• Nonequilibrium transport in mesoscopic multi-terminal SNS Josephson junctions
• Keldysh Ginzburg-Landau action of fluctuating superconductors
• Counterflow of electrons in two isolated quantum point contacts
• Quasiclassical theory of charge transport in disordered interacting electron systems
• Coulomb drag at zero temperature
• Noise in mesoscopic physics
• Energy relaxation in the spin-polarized disordered electron liquid
• Nonlinear Sigma Model for Normal and Superconducting Systems: A Pedestrian Approach
• Josephson current noise above Tc in superconducting tunnel junctions
• Phase-dependent noise correlations in normal-superconducting structures
• The Statistical Theory of Mesoscopic Noise

Cited by in corpus (250)

• Nonequilibrium dynamics of closed interacting quantum systems
• Phase space representation of quantum dynamics
• First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Emergent superfluid crystals, frustration, and topologically defected states in multimode cavity QED
• Unconventional magnetism via optical pumping of interacting spin systems
• Colloquium: Nonequilibrium effects in superconductors with a spin-splitting field
• Quantum critical states and phase transitions in the presence of non equilibrium noise
• Nonequilibrium many-body steady states via Keldysh formalism
• Quantum quench in interacting field theory: a self-consistent approximation
• Nonlinear interaction effects in a strongly driven optomechanical cavity
• Emergent equilibrium in many-body optical bistability
• Current-induced forces in mesoscopic systems: a scattering matrix approach
• Non-equilibrium Functional Renormalization for Driven-Dissipative Bose-Einstein Condensation
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• Electron Cotunneling into a Kondo Lattice
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Decay rates for topological memories encoded with Majorana fermions
• Nonequilibrium Phase Diagram of a Driven-Dissipative Many-Body System
• Probing Majorana Physics in Quantum Dot Shot Noise Experiments
• Theory of free fermions under random projective measurements
• Atom-light crystallization of BECs in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration
• Bosonization of one dimensional fermions out of equilibrium
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Superconductor-Insulator transition and energy localization
• Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space
• Coulomb interaction in graphene: Relaxation rates and transport
• Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids
• Dicke Quantum Spin and Photon Glass in Optical Cavities: Non-equilibrium theory and experimental signatures
• Dynamics and universality in noise driven dissipative systems
• Relativistic fluid dynamics: physics for many different scales
• Visualizing landscapes of the superconducting gap in heterogeneous superconductor thin films: geometric influences on proximity effects
• Effective actions for anomalous hydrodynamics
• Real-Time Dynamics in Quantum Impurity Models with Diagrammatic Monte Carlo
• Dynamical structure factor of the triangular antiferromagnet: the Schwinger boson theory beyond the mean field approach
• Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
• Iterative summation of path integrals for nonequilibrium molecular quantum transport
• Shot noise in a Majorana fermion chain
• Squeezed bispectrum and one-loop corrections in transient constant-roll inflation
• Electron-phonon mediated heat flow in disordered graphene
• Skyrmions Driven by Intrinsic Magnons
• Schwinger-Keldysh formalism II: Thermal equivariant cohomology
• Theory of the strongly disordered Weyl semimetal
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Dimensional Crossover Driven by an Electric Field
• Interference induced thermoelectric switching and heat rectification in quantum Hall junctions
• Fermi-liquid theory for the single-impurity Anderson model
• Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
• SU(3) semiclassical representation of quantum dynamics of interacting spins
• Statistical nature of infrared dynamics on de Sitter background
• Anomalous charge tunneling in the fractional quantum Hall edge states at filling factor ν= 5/2
• Benchmarking the cosmological master equations
• Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
• Cancellation of quantum corrections on the soft curvature perturbations
• Microwave spectroscopy of Josephson junctions in topological superconductors
• Full counting statistics of energy fluctuations in a driven quantum resonator
• Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
• Spin-thermoelectric transport induced by interactions and spin-flip processes in two dimensional topological insulators
• Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
• The Open Effective Field Theory of Inflation
• Full counting statistics of Luttinger liquid conductor
• Quantum feedback at the solid-liquid interface: flow-induced electronic current and its negative contribution to friction
• Bosonization out of equilibrium
• At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model
• Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas
• Transient fluctuation relations for time-dependent particle transport
• Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model
• Environmental induced renormalization effects in quantum Hall edge states
• Non-thermalization in trapped atomic ion spin chains
• Majorana zero modes choose Euler numbers - revealed by full counting statistics
• The Hall Effect in Superconducting Films
• Spin current pumping in helical Luttinger liquids
• Measurement-induced transitions for interacting fermions
• Vacuum Decay in Real Time and Imaginary Time Formalisms
• Noninvasiveness and time symmetry of weak measurements
• Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Transport properties of topological superconductor-Luttinger liquid junctions: a real-time Keldysh approach
• Effective field theory of time-translational symmetry breaking in nonequilibrium open system
• Quantum Boltzmann equation for a mobile impurity in a degenerate Tonks-Girardeau gas
• Neutral modes edge state dynamics through quantum point contacts
• Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
• Real photons from vacuum fluctuations in optomechanics: the role of polariton interactions
• Power law tails and non Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory
• Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Fluctuation conductivity in disordered superconducting films
• The antiferromagnetic phase of the Floquet-driven Hubbard model
• Iterative path integral summation for nonequilibrium quantum transport
• Spectral Form Factor as an OTOC Averaged over the Heisenberg Group
• Quantum echo dynamics in the Sherrington-Kirkpatrick model
• Color Glass Condensate in Schwinger-Keldysh QCD
• Non-Equilibrium Field Theory for Dynamics Starting from Arbitrary Athermal Initial Conditions
• Models of mesoscopic time-resolved current detection
• Excitation Spectra of Bosons in Optical Lattices from Schwinger-Keldysh Calculation
• A perturbative renormalization group approach to driven quantum systems
• Cold bosons in the Landauer setup
• Spectral Representation of Thermal OTO Correlators
• Out of Time Ordered Quantum Dissipation
• Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Out of equilibrium dynamics of classical and quantum complex systems
• Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction
• Levitons in superconducting point contacts
• Nonlinear $\sigma$-model for disordered systems with intrinsic spin-orbit coupling
• Theory of non-equilibrium electronic Mach-Zehnder interferometer
• Duality of Weak and Strong Scatterer in Luttinger liquid Coupled to Massless Bosons
• Migdal-Eliashberg theory as a classical spin chain
• Quantum transport theory for unconventional magnets: Interplay of altermagnetism and p-wave magnetism with superconductivity
• An Open Effective Field Theory for light in a medium
• Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid
• Quasiclassical expressions for the free energy of superconducting systems
• Echo spectroscopy of Anderson localization
• Cancellation of vacuum diagrams and long-time limit in out-of-equilibrium diagrammatic Quantum Monte Carlo
• Dynamic Stimulation of Quantum Coherence in Lattice Bosons
• Solvable model for quantum criticality between Sachdev-Ye-Kitaev liquid and disordered Fermi liquid
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Keldysh approach to periodically driven systems with a fermionic bath: non-equilibrium steady state, proximity effect and dissipation
• Two-Photon Absorption by Impurity Scattering and Amplitude Mode in Conventional Superconductors
• Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation
• Probing Out-of-Time-Order Correlators
• Superconducting critical temperature in the extended diffusive SYK model
• Schwinger-Keldysh path integral for the quantum harmonic oscillator
• Analytically solvable model of an electronic Mach-Zehnder interferometer
• Kinetic Theory for Interacting Luttinger Liquids
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Cavity Higgs-Polaritons
• Heat Current in Non-Markovian Open Systems
• Real-Time Ginzburg-Landau Theory for Bosons in Optical Lattices
• Nonequilibrium functional bosonization of quantum wire networks
• Functional field integral approach to quantum work
• Magnon-induced non-Markovian friction of a domain wall in a ferromagnet
• Relaxation dynamics of the electron distribution in the Coulomb blockade problem
• Realization of the $\pi$-state in junctions formed by multi-band superconductors with a spin-density-wave
• Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
• Topological Anomalous Skin Effect in Weyl Superconductors
• Delta-T noise for fractional quantum Hall states at different filling factor
• Bath-induced spin inertia
• Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling
• Non-equilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions
• Giant current fluctuations in an overheated single electron transistor
• Quantum Brownian Motion of a Magnetic Skyrmion
• Keldysh formalism for multiple parallel worlds
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Spin Hall and inverse spin galvanic effects in graphene with strong interfacial spin-orbit coupling: a quasi-classical Green's function approach
• Transport properties of fully screened Kondo models
• A random phase approximation study of one-dimensional fermions after a quantum quench
• Dephasing of Cooper pairs and subgap electron transport in superconducting hybrids
• Transport theory of superconductors with singular interaction corrections
• Renyi Entropy of Interacting Thermal Bosons in Large $N$ Approximation
• The Loschmidt Spectral Form Factor
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Multiple Andreev reflections in s-wave superconductor-quantum dot- topological superconductor tunnel junctions and Majorana bound states
• Nonequilibrium quantum criticality in bilayer itinerant ferromagnets
• Relativistic invariance of the vacuum
• Nonequilibrium charge transport through Falicov-Kimball structures connected to metallic leads
• Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors
• Nonequilibrium quantum dynamics of the magnetic Anderson model
• Finite-temperature conductance of strongly interacting quantum wire with a nuclear spin order
• Relaxation of photoexcitations in polaron-induced magnetic microstructures
• Shot noise in Graphene with long range Coulomb interaction and the local Fermi distribution
• Quantum gray solitons in confining potentials
• 4-point correlators in finite-temperature AdS/CFT: jet quenching correlations
• Non-equilibrium scalar field dynamics starting from Fock states: Absence of thermalization in one dimensional phonons coupled to fermions
• Memories of initial states and density imbalance in dynamics of interacting disordered systems
• Double Quantum Dot scenario for spin resonance in current noise
• On non-equilibrium photon distributions in the Casimir effect
• Out-of-equilibrium heating of electron liquid: fermionic and bosonic temperatures
• Theory of temperature fluctuation statistics in superconductor-normal metal tunnel structures
• Geometric and algebraic approaches to quantum theory
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Spin pumping and torque statistics in the quantum noise limit
• Nonequilibrium noise and current fluctuations at the superconducting phase transition
• Dynamics and Charge Fluctuations in Large-q Sachdev-Ye-Kitaev Lattices
• Renormalization in Open Quantum Field theory I: Scalar field theory
• Noise of a chargeless Fermi liquid
• Mode attraction in Floquet systems with memory: application to magnonics
• Inclusive scattering matrix and scattering of quasiparticles
• High-frequency vibrational density of states of a disordered solid
• Transient effects in the backscattered current of a Luttinger liquid
• Josephson currents in chaotic quantum dots
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Suppression of Shot Noise in a Dirty Marginal Fermi Liquid
• Nanoscopic interferometer model for spin resonance in current noise
• Ultrasonic attenuation via energy diffusion channel in disordered conductors
• Effective Thermal Physics in Holography: A Brief Review
• N-particle irreducible actions for stochastic fluids
• Transport through single-level systems: Spin dynamics in the nonadiabatic regime
• A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current
• Magnetoelectric effects in diffusive two-dimensional superconductors studied by the nonlinear $\sigma$ model
• Out-of-Equilibrium Admittance of Single Electron Box Under Strong Coulomb Blockade
• Scattering matrix and inclusive scattering matrix in algebraic quantum field theory
• Early-Time and Late-Time Quantum Chaos
• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid
• Supercurrent dephasing by electron-electron interactions
• Diffusive modes of two-band fermions under number-conserving dissipative dynamics
• Current fluctuations in composite conductors: Beyond the second cumulant
• Theory for electrical detection of the magnon Hall effect induced by dipolar interactions
• Transient Features in Charge Fractionalization, Local Equilibration and Non-equilibrium Bosonization
• Energy relaxation rate and its mesoscopic fluctuations in quantum dots
• Thermodynamics and dynamics of coupled complex SYK models
• Dynamics of magnetic moments coupled to electrons and lattice oscillations
• Dynamical Hall responses of disordered superconductors
• Quantum cosmology of the flat universe via closed real-time path integral
• Non-Markovian dephasing of disordered, quasi-one-dimensional fermion systems
• Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach
• The influence of interaction between quasiparticles on parametric resonance process in Bose-Einstein condensates
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Quantum-field-theoretical approach to phase-space techniques: Symmetric Wick theorem and multitime Wigner representation
• Path Integral Formalism for Quantum Open Systems
• Pairing Fluctuation AC Conductivity of Disordered Thin Films
• Non-linear quantum critical dynamics and fluctuation-dissipation ratios far from equilibrium
• Spin correlation functions and quasiparticle decay
• Far-from-equilibrium superconductor in fluctuational regime
• Dyson-Schwinger equation approach to Lorentz Symmetry Breaking with finite temperature and chemical potential
• Keldysh Derivation of Oguri's Linear Conductance Formula for Interacting Fermions
• Quantum quench, large N, and symmetry restoration
• Nonlinear sigma model for optical media with linear absorption or gain
• Fluctuation-driven excess noise near superconducting phase transition
• Fluctuation-induced noise in out-of-equilibrium disordered superconducting films
• Real-time quantum dynamics, path integrals and the method of thimbles
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
• Quantum noise in the spin transfer torque effect
• Absence of localization in Weyl semimetals
• Thermal transport in disordered one-dimensional spin chains
• Duality and bosonization in Schwinger-Keldysh formulation
• Spin Hall conductivity of interacting two-dimensional electron systems
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Work Statistics and Adiabatic Assumption in Nonequilibrium Many-Body Theory
• Elusive phase transition in the replica limit of monitored systems
• Spatially resolved collective modes in d-wave superconductors
• Transient and finite size effects in transport properties of a quantum wire
• The effect of superconducting fluctuations on the ac conductivity of a 2D electron system in the diffusive regime
• Attempt to describe phase slips by means of an adiabatic approximation
• Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid
• Electrical magnetochiral anisotropy in Rashba superconductors
• Pumping current of a Luttinger liquid with finite length
• Resonant second harmonic generation in a two-dimensional electron system
• Weak localization correction to linear absorption in conventional superconductors
• Fine structure of current noise spectra in nanoelectromechanical resonators
• Decoherence of Cooper pairs and subgap magnetoconductance of superconducting hybrids
• Superfluid density of a photo-induced superconducting state
• Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions
• Magnetoelectric effects in superconductors due to spin-orbit scattering: a non-linear $\sigma$-model description
• Constrained motions and slow dynamics in one-dimensional bosons with double-well dispersion
• Quantum theory of an electromagnetic observer: classically behaving macroscopic systems and emergence of classical world in quantum electrodynamics