Multimode Brownian oscillators: Exact solutions to heat transport

TL;DR

This paper develops an algebraic method to exactly solve heat transport in multimode Brownian oscillators coupled to multiple reservoirs, providing insights into nonequilibrium quantum thermodynamics.

Contribution

It introduces an exact algebraic approach for analyzing heat transport in multimode Brownian oscillators under nonequilibrium conditions.

Findings

Steady-state heat current matches existing numerical methods.

Exact time-local equations of motion derived for reduced density operators.

Method enhances understanding of open quantum system dynamics.

Abstract

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local equation of motion for reduced density operator, from which we can easily extract not only the reduced system but also hybrid bath dynamical information. The resulted steady-state heat current is found numerically consistent with another discrete imaginary-frequency method followed by the Meir-Wingreen's formula. It is anticipated that the development in this work would constitute an indispensable component to nonequilibrium statistical mechanics for open quantum systems.