Large Deviations and Fluctuation Theorem for the Quantum Heat Current

TL;DR

This paper derives an explicit generating function for heat flow in a quantum system, demonstrating fluctuation theorems and fluctuation-dissipation relations, supported by numerical results.

Contribution

It provides a new analytical expression for the heat current generating function in a quantum harmonic oscillator system under the NIBA approximation, confirming fluctuation theorems.

Findings

The generating function satisfies the Gallavotti-Cohen fluctuation theorem.

Heat conductivity is proportional to the variance of the heat current.

Numerical results support the theoretical findings.

Abstract

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the hot and cold baths is derived by evaluating the corresponding Feynman-Vernon path integral under the non-interacting blip approximation (NIBA). This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductivity is proportional to the variance of the heat current, retrieving the well known fluctuation dissipation relation. Finally, we present numerical results for the heat current.