Distribution Function of Electron Velocity Perpendicular to the Driving Force in a Uniform Nonequilibrium Steady State

TL;DR

This study uses molecular dynamics to determine the velocity distribution function of electrons perpendicular to an external force in a nonequilibrium steady state, revealing deviations from local equilibrium but similar tail behavior to Maxwell distribution.

Contribution

The paper provides an explicit form of the electron velocity distribution function in a nonequilibrium steady state, extending understanding beyond local equilibrium assumptions.

Findings

The distribution function fits numerical data well even outside local equilibrium.

Tail behavior of the distribution matches a Maxwell distribution with an effective temperature.

The explicit form of the distribution function is determined within simulation accuracy.

Abstract

A macroscopically uniform model of a two-dimensional electron system is proposed to study nonequilibrium properties of electrical conduction. By molecular dynamics simulation, the steady state distribution function $P_y$ of electron velocity in a direction perpendicular to an external driving force is calculated. An explicit form of $P_y$ is determined within the accuracy of the numerical simulation, which fits the numerical data well even in the regime where a local equilibrium description is not valid. Although the entire structure of $P_y$ is different from that of a local equilibrium distribution function, the asymptotic structure of the tails of $P_y$ in the limit of large absolute values of the velocity is identical to that of a Maxwell distribution function with a temperature which is different from that in the equilibrium state and the kinetic temperature in the steady state.