Local temperature and chemical potential inside a mesoscopic device driven out of equilibrium

TL;DR

This paper presents a method to calculate local temperature and chemical potential in mesoscopic devices out of equilibrium, analyzing how these variables behave under disorder and interactions.

Contribution

It introduces a novel approach to determine local thermodynamic variables in non-equilibrium mesoscopic systems, including effects of disorder and electron-electron interactions.

Findings

Large fluctuations in onsite chemical potentials due to disorder

Electron-electron interactions suppress chemical potential fluctuations

Classical voltage drop profile recovered after disorder averaging

Abstract

In this paper we introduce a method of calculating the local temperature and chemical potential inside a mesoscopic device out of equilibrium. We show how to check the conditions of local thermal equilibrium as the whole system is out of equilibrium. Especially we study the onsite chemical potentials inside a chain coupled to two reservoirs at a finite voltage bias. In the presence of disorder we observe a large fluctuation in onsite chemical potentials, which can be suppressed by the electron-electron interaction. By taking average with respect to the configurations of disorder, we recover the classical picture where the voltage drops monotonously through the resistance wire. We prove the existence of local intensive variables in a mesoscopic device which is in equilibrium or not far from equilibrium.