Quantum Equilibration under Constraints and Transport Balance

TL;DR

This paper extends quantum equilibration theory to include conserved quantities like particle number, showing how systems reach equilibrium characterized by temperature and chemical potential, even with multiple baths and non-thermal states.

Contribution

It generalizes quantum equilibration to systems with conserved quantities and multiple baths, revealing conditions for non-thermal steady states and potential for engineered quantum states.

Findings

Systems equilibrate with temperature and chemical potential when coupled to a bath with these parameters.

Multiple baths can lead to non-thermal steady states that resemble a single averaged bath.

Under certain conditions, the stationary state is described by a Boltzmann factor.

Abstract

For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath inverse temperature $\beta$. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature $\beta$ and chemical potential $\mu$ we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general non-thermal bath, which may be exploited to generate desired non-thermal states. Under special circumstances the stationary state may be again be described by a unique Boltzmann factor. These results are illustrated by several examples.