Hamiltonian of mean force for damped quantum systems

TL;DR

This paper investigates how the stationary state of a damped quantum harmonic oscillator deviates from the standard Gibbs distribution due to finite system-reservoir coupling, using the quantum Hamiltonian of mean force for exact and approximate analysis.

Contribution

It provides an exact quantification of the deviation from Gibbs form for a damped quantum oscillator using the Hamiltonian of mean force, including approximations across temperature and coupling regimes.

Findings

Deviation from Gibbs distribution quantified for finite coupling.

Approximate results derived for high/low temperatures and weak/strong couplings.

Physical interpretation of the deviation in terms of initial system-reservoir coupling.

Abstract

We consider a quantum system linearly coupled to a reservoir of harmonic oscillators. For finite coupling strengths, the stationary distribution of the damped system is not of the Gibbs form, in contrast to standard thermodynamics. With the help of the quantum Hamiltonian of mean force, we quantify this deviation exactly for a harmonic oscillator and provide approximations in the limit of high and low temperatures, and weak and strong couplings. Moreover, in the semiclassical regime, we use the quantum Smoluchowski equation to obtain results valid for any potential. We, finally, give a physical interpretation of the deviation in terms of the initial system-reservoir coupling.