Nonequilibrium Green's functions in the study of heat transport of driven nanomechanical systems

TL;DR

This paper reviews a Green's function approach to analyze heat transport in driven nanomechanical systems, highlighting how ac forces influence energy flow and can function as quantum engines.

Contribution

It introduces a Green's function formalism for heat transport in driven phononic systems and explores energy exchange mechanisms under ac driving.

Findings

Green's functions enable calculation of heat currents and power in driven systems.

Ac forces can generate heat and also act as quantum engines exchanging energy.

Strategies for exact and approximate Green's function evaluation are discussed.

Abstract

We review a recent theoretical development based on non-equilibrium Green's function formalism to study heat transport in nanomechanical devices modeled by phononic systems of coupled quantum oscillators driven by ac forces and connected to phononic reservoirs. We present the relevant equations to calculate the heat currents flowing along different regions of the setup, as well as the power developed by the time-dependent forces. We also present different strategies to evaluate the Green's functions exactly or approximately within the weak driving regime. We finally discuss the different mechanisms in which the ac driving forces deliver the energy. We show that, besides generating heat, the forces may operate exchanging energy as a quantum engine.