Another Return of 'Return to Equilibrium'

Abstract

The property of ``{\it return to equilibrium}'' is established for a class of quantum-mechanical models describing interactions of a (toy) atom with black-body radiation, or of a spin with a heat bath of scalar bosons, under the assumption that the interaction strength is {\it sufficiently weak}. For models describing the first class of systems, our upper bound on the interaction strength is {\it independent} of the temperature $T$, (with $0<T\le T_0<\infty$), while, for the spin-boson model, it tends to zero logarithmically, as $T\to 0$. Our result holds for interaction form factors with physically realistic infrared behaviour. Three key ingredients of our analysis are: a suitable concrete form of the Araki-Woods representation of the radiation field, Mourre's positive commutator method combined with a recent virial theorem, and a norm bound on the difference between the equilibrium states of the interacting and the non-interacting system (which, for the system of an atom coupled to black-body radiation, is valid for {\it all} temperatures $T\ge 0$, assuming only that the interaction strength is sufficiently weak).

References in corpus (5)

• Positive Commutators in Non-Equilibrium Statistical Mechanics
• Thermal Ionization
• Ionization of Atoms in a Thermal Field
• The Stability of the Non-Equilibrium Steady States
• Ergodic Properties of the Spin - Boson System

Cited by in corpus (30)

• Strong Coupling Thermodynamics of Open Quantum Systems
• Open quantum system dynamics and the mean force Gibbs state
• Non-equilibrium equalities with unital quantum channels
• Decoherence and Thermalization
• Resonance Theory of Decoherence and Thermalization
• 'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
• Dynamics of Open Quantum Systems II, Markovian Approximation
• Adaiabtic theorems and reversible isothermal processes
• On the irreversible dynamics emerging from quantum resonances
• Regularity of Bound States
• Dynamics of Open Quantum Systems I, Oscillation and Decay
• Ergodicity of the Spin-Boson Model for arbitrary coupling strength
• Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate
• Quantum Brownian Motion in a Simple Model System
• A note on the Landauer principle in quantum statistical mechanics
• Steady state in ultrastrong coupling regime: perturbative expansion and first orders
• Stability of Equilibria with a Condensate
• Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments
• Mixing properties of the one-atom maser
• Completely positive dynamical semigroups and quantum resonance theory
• Entanglement Evolution via Quantum Resonances
• Overlapping Resonances in Open Quantum Systems
• Open-system eigenstate thermalization in a noninteracting integrable model
• A resonance theory for open quantum systems with time-dependent dynamics
• Equivalence between the second order steady state for the spin-Boson model and its quantum mean force Gibbs state
• Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization
• Entropic Fluctuation Theorems for the Spin-Fermion Model
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
• Thermal Ionization for Short-Range Potentials
• Miniatures on Open Quantum Systems