Hybrid quantum-classical dynamics with stationary thermal states

TL;DR

This paper investigates the conditions under which hybrid quantum-classical dynamics converge to a thermal state, identifying specific equations that satisfy detailed balance and illustrating effects of coupling on subsystem states.

Contribution

It characterizes hybrid Lindblad equations that lead to thermal stationary states, expanding understanding of quantum-classical thermalization mechanisms.

Findings

A subclass of hybrid Lindblad equations satisfies the detailed balance condition.

Coupling can transform a Gaussian thermal state into a bimodal distribution.

Examples show how subsystem thermal states are affected by mutual interaction.

Abstract

Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is, a density matrix that maximizes the hybrid arrangement entropy under the constraints of a canonical ensemble. Introducing a detailed balance condition, it is found that a specific subclass of hybrid Lindblad equations fulfill the demanded requirement. The main theoretical results are exemplified through a set of specific examples that in addition lighten how the thermal state of each subsystem in isolation is affected by their mutual coupling. In particular, a Gaussian thermal state could become a bimodal distribution when increasing the interaction strength of a classical subsystem with a quantum two-level subsystem.