Plyukhin A V
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 1):061136. doi: 10.1103/PhysRevE.77.061136. Epub 2008 Jun 26.
Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass m<<M is considered beyond lowest order in the mass ratio mM . The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In the general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order (m/M)2 and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented.
考虑质量为(M)的粒子在质量为(m\ll M)的分子浴中的布朗运动的微观理论，超出了质量比(m/M)的最低阶。相应的朗之万方程包含对耗散力的非线性修正，广义福克 - 普朗克方程涉及高于二阶的导数。这些方程从第一原理导出，系数用粒子上微观力的相关函数表示。对于具有有限分子 - 粒子碰撞时间的广义瑞利模型，明确评估了系数。在低密度浴的极限情况下，我们恢复了先前针对具有瞬时二元碰撞的模型获得的结果。在一般情况下，方程包含源自有限碰撞时间的额外修正，与浴密度成二次关系。这些修正保留到((m/M)^2)阶，并发现使平稳分布非麦克斯韦分布。还给出了一些相关的数值模拟。
