Langevin equation for the extended Rayleigh model with an asymmetric bath.
Langevin equation for the extended Rayleigh model with an asymmetric bath.
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具有不对称浴的扩展瑞利模型的 Langevin 方程。
DOI：
10.1103/physreve.69.021112
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Schofield
中科院分区：
文献类型：
--
作者：
A. Plyukhin;J. Schofield
本文考虑了一个由可移动的重型活塞分离的两个无限大气体的一维模型。对于活塞左右两侧气体颗粒的热力学参数和/或分子质量不同的情况，从第一原理出发，导出了活塞运动的非线性朗之万方程。对于出现在非线性朗之万方程中的所有参数，得到了熔池粒子与活塞之间作用力的时间关联函数的微观表达式。证明了在没有系统力的情况下，该方程存在与方向涨落引起的漂移相对应的定常解。在理想气体通过二次排斥势与活塞相互作用的情况下，该模型是精确可解的，并导出了非线性朗之万方程中动力学系数的显式表达式。对非线性朗之万方程的暂态解进行了微扰分析，证明了已有的关于硬壁相互作用系统的结果得到了恢复。
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the nonlinear Langevin equation are derived. The transient solution of the nonlinear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.