Theory of Non-Equilibrium Sationary States as a Theory of Resonances

Abstract

We study a small quantum system (e.g. a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states, parametrized by two numbers $T_1$, $T_2$ (``reservoir temperatures''). If $T_1\ne T_2$, then these states are non-equilibrium, stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production. Furthermore, we show that these states are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures $T_1$ and $T_2$, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound $\min (T_1,T_2)>g^{2+\alpha }$, where $g$ is the coupling constant and $0<\alpha <1$ is a power related to the infra-red behaviour of the coupling functions.

arXiv comment1 figure. To appear in Ann. H. Poincare

References in corpus (9)

• Entropy production in quantum spin systems
• Dissipative Transport: Thermal Contacts and Tunnelling Junctions
• Positive Commutators in Non-Equilibrium Statistical Mechanics
• Natural nonequilibrium states in quantum statistical mechanics
• Thermal Ionization
• How should one define entropy production for nonequilibrium quantum spin systems?
• Topics in quantum statistical mechanics and operator algebras
• Stability of Equilibria with a Condensate
• Cyclic thermodynamic processes and entropy production

Cited by in corpus (22)

• Repeated interactions in open quantum systems
• Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production
• Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
• Dynamics of Collective Decoherence and Thermalization
• Random repeated interaction quantum systems
• On the steady state correlation functions of open interacting systems
• A note on the Landauer principle in quantum statistical mechanics
• A mathematical account of the NEGF formalism
• Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems
• Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light I - The Effective Theory
• Overlapping Resonances in Open Quantum Systems
• A resonance theory for open quantum systems with time-dependent dynamics
• Fermionic walkers driven out of equilibrium
• Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization
• Entropic Fluctuation Theorems for the Spin-Fermion Model
• A Geometric Approach to the Landauer-Büttiker Formula
• Probing non-equilibrium steady states of the Klein-Gordon field with Unruh-DeWitt detectors
• Fully Coupled Pauli-Fierz Systems at Zero and Positive Temperature
• Full statistics of erasure processes: Isothermal adiabatic theory and a statistical Landauer principle
• A rigorous derivation of the transition rate for the dissipative two-state system
• 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
• Miniatures on Open Quantum Systems