Multimode Brownian oscillators: Exact solutions to heat transport

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 the reduced density operator, from which we can easily extract not only the reduced system but also hybrid bath dynamical information. The resulting steady-state heat current is found to be numerically consistent with another discrete imaginary-frequency method followed by Meir–Wingreen’s formula. It is anticipated that the development in this work would constitute an indispensable component of nonequilibrium statistical mechanics for open quantum systems.