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

TL;DR

This paper develops a theoretical framework for understanding non-equilibrium stationary states (NESS) in small quantum systems coupled to reservoirs at different temperatures, demonstrating their stability and physical properties.

Contribution

It introduces a rigorous analysis of NESS in quantum systems interacting with reservoirs, including stability, heat flux, and entropy production, under specific temperature and coupling conditions.

Findings

Existence of a family of NESS parametrized by reservoir temperatures.

Non-zero heat fluxes and positive entropy production in NESS.

Dynamical asymptotic stability of the stationary states.

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 $T_1\neq T_2$, 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.