Approach to equilibrium in translation-invariant quantum systems: some structural results

DOI10.1007/s00023-023-01281-6arXiv2204.00440MaRDI QIDQ6191562

Vojkan Jakšić, Clément Tauber, Claude-Alain Pillet

Publication date: 9 February 2024

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.00440

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46Lxx) Equilibrium statistical mechanics (82Bxx) Time-dependent statistical mechanics (dynamic and nonequilibrium) (82Cxx)

Related Items (1)

Adiabatic evolution of low-temperature many-body systems

Cites Work

• Weakly nonlinear Schrödinger equation with random initial data
• `Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
• Non-uniform specification and large deviations for weak Gibbs measures
• The origins of time-asymmetry in thermodynamics: the minus first law
• Unitary equivalence of temperature dynamics for ideal and locally perturbed Fermi-gas
• Another return of ``Return to equilibrium
• The Green-Kubo formula and the Onsager reciprocity relations in quantum statistical mechanics
• Instability of equilibrium states for coupled heat reservoirs at different temperatures
• The Green-Kubo formula for the spin-Fermion system
• Markovian master equations
• Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
• Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs
• On the algebra of fluctuation in quantum spin chains
• Mathematical theory of non-equilibrium quantum statistical mechanics
• Return to equilibrium for Pauli-Fierz systems
• Dissipative transport: thermal contacts and tunnelling junctions
• The stability of the nonequilibrium steady states
• Almost Gibbsian versus weakly Gibbsian measures
• Relative entropy and variational properties of generalized Gibbsian measures.
• On a model for quantum friction. III: Ergodic properties of the spin -- boson system
• Natural nonequilibrium states in quantum statistical mechanics
• Entropic fluctuations of quantum dynamical semigroups
• On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence
• Perturbation theory of KMS states
• On the quantum Boltzmann equation
• The Green-Kubo formula for locally interacting fermionic open systems
• Quantum information theory and quantum statistics.
• Theory of non-equilibrium stationary states as a theory of resonances
• A short review on the derivation of the nonlinear quantum Boltzmann equations
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• Linear response theory for thermally driven quantum open systems
• On the equilibrium states in quantum statistical mechanics
• Statistica mechanics of quantum spin systems. III
• Gibbs states of a one dimensional quantum lattice
• Asymptotic orbits in a free Fermi gas
• Large deviations in quantum lattice systems: one-phase region
• Gibbs variational formula for thermal equilibrium states in terms of quantum relative entropy density
• QUANTUM HYPOTHESIS TESTING AND NON-EQUILIBRIUM STATISTICAL MECHANICS
• RUELLE–LANFORD FUNCTIONS AND LARGE DEVIATIONS FOR ASYMPTOTICALLY DECOUPLED QUANTUM SYSTEMS
• Multifractal analysis of weak Gibbs measures for non-uniformly expanding C¹ maps
• Transport properties of quasi-free fermions
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• ENTROPY DENSITIES FOR GIBBS STATES OF QUANTUM SPIN SYSTEMS
• Spectral theory of thermal relaxation
• KMS, ETC.
• Weak Gibbs measures and the local product structure
• Asymptotic decoupling and weak Gibbs measures for finite alphabet shift spaces
• On the relation between Gibbs and -measures
• Some properties of correlations of quantum lattice systems in thermal equilibrium
• Quantum Dynamical Systems
• Topics in Non-Equilibrium Quantum Statistical Mechanics
• Fermi Golden Rule and Open Quantum Systems
• Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States
• VARIATIONAL PRINCIPLE FOR NON-EQUILIBRIUM STEADY STATES OF THE XX MODEL
• LARGE DEVIATION GENERATING FUNCTION FOR CURRENTS IN THE PAULI–FIERZ MODEL
• Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction
• States of Classical Statistical Mechanics
• EQUILIBRIUM STATISTICAL MECHANICS OF FERMION LATTICE SYSTEMS
• Return to equilibrium
• Return to equilibrium
• Entropy production in quantum spin systems
• A note on eigenvalues of Liouvilleans
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Approach to equilibrium in translation-invariant quantum systems: some structural results