Quantum thermodynamics of nonadiabatically driven systems: The effect of electron-phonon interaction

TL;DR

This paper investigates how nonadiabatic external driving influences the thermodynamics of an electron-phonon system, using perturbative and numerical methods to analyze charge transport and vibrational dynamics.

Contribution

It introduces a detailed comparison between perturbative corrections and hierarchical equations of motion for nonadiabatic quantum thermodynamics.

Findings

Nonadiabatic corrections affect electronic populations and charge currents.

Electronic friction indicates Franck-Condon and non-resonant tunneling effects.

HEOM provides accurate results across coupling and driving regimes.

Abstract

In this work we study the effects of nonadiabatic external driving on the thermodynamics of an electronic system coupled to two electronic leads and to a phonon mode, with and without damping. In the limit of slow driving, we establish nonadiabatic corrections to quantum thermodynamic quantities. In particular, we study the first-order correction to the electronic population, charge-current, and vibrational excitation using a perturbative expansion, and compare the results to the numerically exact hierarchical equations of motion (HEOM) approach. Furthermore, the HEOM analysis spans both the weak and strong system-bath coupling regime and the slow and fast driving limits. We show that the electronic friction and the nonadiabatic corrections to the charge-current provide a clear indicator for the Franck-Condon effect and for non-resonant tunneling processes. We also discuss the validity of the approximate quantum master equation approach and the benefits of using HEOM to study quantum thermodynamics out of equilibrium.