Field Theory of Many-Body Lindbladian Dynamics

Abstract

We review and further develop the Keldysh functional integral technique for the study of Lindbladian evolution of many-body driven-dissipative quantum systems. A systematic and pedagogical account of the dynamics of generic bosonic and fermionic Lindbladians is presented. Our particular emphasis is on unique properties of the stationary distribution function, determined by the Lyapunov equation. This framework is applied to study examples of Lindbladian dynamics in the context of band theory, disorder, collisionless collective modes, and mean-field theory.

References in corpus (25)

• Probing many-body dynamics on a 51-atom quantum simulator
• Quantum fluids of light
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Cold atoms in cavity-generated dynamical optical potentials
• Quantum trajectories and open many-body quantum systems
• Exciton-polariton condensates
• Bose-Einstein condensation of photons in an optical microcavity
• Excitations in a non-equilibrium Bose-Einstein condensate of exciton-polaritons
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Spontaneous rotating vortex lattices in a pumped decaying condensate
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Engineered Dissipation for Quantum Information Science
• Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons
• Switching via quantum activation: A parametrically modulated oscillator
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Fermionic Gaussian states: an introduction to numerical approaches
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
• Lindbladian dissipation of strongly-correlated quantum matter
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• Exact solutions of interacting dissipative systems via weak symmetries

Cited by in corpus (30)

• Universality in driven open quantum matter
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Many-Body Open Quantum Systems
• The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model
• Designing open quantum systems with known steady states: Davies generators and beyond
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Linear and Non-Linear Response of Quadratic Lindbladians
• Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries
• Diffusive modes of two-band fermions under number-conserving dissipative dynamics
• Population Dynamics of Schrödinger Cats
• Localization of Lindbladian Fermions
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Dissipative phase transition of interacting non-reciprocal fermions
• Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator
• Path Integral Approach to Input-Output Theory
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Kinetics of Quantum Reaction-Diffusion systems
• The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation
• Simulating electron-vibron energy transfer with quantum dots and resonators
• Non-Hermitian Dirac theory from Lindbladian dynamics
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Chiral Instabilities in Driven-Dissipative Quantum Liquids
• Spectroscopic Signatures of a Liouvillian Exceptional Spectral Phase in a Collective Spin
• Physical constraints on effective non-Hermitian systems