Second-order adiabatic expansions of heat and charge currents with nonequilibrium Green's functions

TL;DR

This paper develops second-order adiabatic expansions for heat and charge currents using nonequilibrium Green's functions, enabling advanced analysis of quantum thermodynamic phenomena in nanoscale systems.

Contribution

It introduces a novel second-order adiabatic expansion framework for currents using nonequilibrium Green's functions, extending beyond first-order approximations.

Findings

Formulas produce physically consistent results

Enable thermodynamic analysis of second-order monoparametric pumping

Illustrated with simple models demonstrating applicability

Abstract

Due to technological needs, nanoscale heat management, energy conversion and quantum thermodynamics have become key areas of research, putting heat pumps and nanomotors center stage. The treatment of these particular systems often requires the use of adiabatic expansions in terms of the frequency of the external driving or the velocity of some classical degree of freedom. However, due to the difficulty of getting the expressions, most works have only explored first-order terms. Despite this, adiabatic expansions have allowed the study of intriguing phenomena such as adiabatic quantum pumps and motors, or electronic friction. Here, we use nonequilibrium Green's functions, within a Schwinger-Keldysh approach, to develop second-order expressions for the energy, heat, and charge currents. We illustrate, through two simple models, how the obtained formulas produce physically consistent results, and allow for the thermodynamic study of unexplored phenomena, such as second-order monoparametric pumping.