Size effects in the long-time quasi-static heat transport

TL;DR

This paper investigates how finite size effects influence heat transfer in quantum systems with finite modes, deriving general expressions and approximate solutions for long-time heat transport between reservoirs.

Contribution

It introduces a generalized quantum Langevin equation approach to analyze finite mode effects on heat transfer, providing new analytical expressions for long-time heat current and temperature relaxation.

Findings

Derived a general expression for heat current in finite mode reservoirs.

Obtained approximate analytical solutions for long-time temperature relaxation.

Identified the impact of mode spacing on heat transfer dynamics.

Abstract

We consider finite size effects on heat transfer between thermal reservoirs mediated by a quantum system, where the number of modes in each reservoir is finite. Our approach is based on the generalized quantum Langevin equation and the thermal reservoirs are described as ensembles of oscillators within the Drude-Ullersma model. A general expression for the heat current between the thermal reservoirs in the long-time quasi-static regime, when an observation time is of the order of $\Delta ^{-1}$ and $\Delta$ is the mode spacing constant of a thermal reservoir, is obtained. The resulting equations that govern the long-time relaxation for the mode temperatures and the average temperatures of the reservoirs are derived and approximate analytical solutions are found.