Heat distribution of a quantum harmonic oscillator

TL;DR

This paper analytically investigates the heat exchange statistics of a quantum harmonic oscillator coupled to a heat bath, verifying fluctuation theorems and analyzing heat distribution over time.

Contribution

It provides an exact analytical computation of the heat distribution characteristic function and explores its behavior in different temperature regimes and thermalization times.

Findings

Verifies the Jarzynski-Wójcik fluctuation theorem for the system

Derives the heat probability density in long thermalization limit

Analyzes the evolution of heat distribution's cumulants over time

Abstract

We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We exactly compute the characteristic function of the heat distribution and show that it verifies the Jarzynski-W\'ojcik fluctuation theorem. We further evaluate the heat probability density in the limit of long thermalization times, both in the low and high temperature regimes, and investigate its time evolution by calculating its first two cumulants.