Distribution Function of Electron Velocity Perpendicular to the Driving Force in a Uniform Nonequilibrium Steady State
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.
Many recent works are devoted to the study of high frequency oscillatory nonlinear waves, and to nonlinear geometric optics. Typical questions are the existence, the propagation, the interaction and the reflection of waves of the form ::: ::: $$ {u^\varepsilon }\left( {t,x} \right) \sim \underline u \left( {t,x} \right) + {\varepsilon ^\alpha }\sum\limits_{n0} {{\varepsilon ^n}} {U_n}\left( {t,x,\varphi \left( {t,x} \right)/\varepsilon } \right). $$ ::: ::: (1.1)