标题： 非平衡稳态解在场中的温度控制玻尔兹曼方程 显示英文标题

标题： Nonequilibrium Stationary Solutions of Thermostated Boltzmann Equation in a Field

摘要： 我们考虑一个受到均匀外部力E作用并经历与“虚拟”固定障碍物随机碰撞的粒子系统，如导电性的Drude模型所示。 系统通过高斯温控器维持在一个非平衡稳态中。 在合适的极限下，系统由一个自洽的玻尔兹曼方程描述，该方程用于单粒子分布函数f。我们发现，经过长时间后，f(v,t)趋近于一个稳态速度分布f(v)，该分布对于高速度为零，即： f(v)=0 当 |v|>vmax(E)，其中vmax(E)~1/|E| 当 |E| -> 0。 在该极限下，对于固定的v，f(v)~exp(-c|v|^3)，其中c依赖于粒子的平均自由程。 f(v)在二维情况下被显式计算。 显示英文摘要

摘要： We consider a system of particles subjected to a uniform external force E and undergoing random collisions with "virtual" fixed obstacles, as in the Drude model of conductivity. The system is maintained in a nonequilibrium stationary state by a Gaussian thermostat. In a suitable limit the system is described by a self consistent Boltzmann equation for the one particle distribution function f. We find that after a long time f(v,t) approaches a stationary velocity distribution f(v) which vanishes for large speeds, i.e. f(v)=0 for |v|>vmax(E), with vmax(E)~1/|E| as |E| -> 0. In that limit f(v)~exp(-c|v|^3) for fixed v, where c depends on mean free path of the particle. f(v) is computed explicitly in one dimension.