大学物理 ›› 2019, Vol. 38 ›› Issue (8): 1-.doi: 10.16854 /j.cnki.1000-0712.180599

• 教学研究 •    下一篇

布朗粒子动量关联函数的若干注记

包景东   

  1. 北京师范大学物理学系,北京100875
  • 收稿日期:2018-10-30 修回日期:2019-04-15 出版日期:2019-08-20 发布日期:2019-09-11
  • 作者简介:作者简介: 包景东( 1962—) ,男,辽宁瓦房店人,北京师范大学物理学系教授,博士,主要从事热力学与统计物理、力学和批判性科学思维的教学; 统计物理、核理论及计算物理的研究工作.
  • 基金资助:
    国家自然科学重点基金( 11735005) 资助

Several notes on the momentum correlation function of a Brownian particle

BAO Jing-dong   

  1. Department of Physics,Beijing Normal University,Beijing 100875,China
  • Received:2018-10-30 Revised:2019-04-15 Online:2019-08-20 Published:2019-09-11

摘要: 布朗粒子的动量关联函数是非平衡统计力学的一个极为重要的物理量,然而国内常用教材对其及相关内容的讲解存在瑕疵.本文从学术研究的角度,对有关动量关联函数的一些不严谨表述进行了厘清.目前的非平衡统计教学皆以含白噪声的朗之万方程为模型,但很难明晰布朗运动中的两个特征时间: 涨落力关联时间和系统驰豫时间.本文以Ornstein-Uhlenbeck色噪声驱动的广义朗之万方程为例解决了这一问题.还讨论了判断各态历经变量的Khinchin 定理,进而深化了动量关联函数的价值.

关键词: 布朗运动, 动量关联函数, 广义朗之万方程, 非各态历经

Abstract: The momentum correlation functuin is a very important physical quantity in non-equilibrium statistical mechanics.However,where are a few errors for the explain of this function and related contents in our usual textbooks.This paper starts from academic research and discusses those un-rigorous descriptions.The Langevin equation subjected to a white noise is regarded as a model in the present textbooks,but it is difficulty for clearing two characteristic times in the Brownian motion: the correlation time of random force and relaxation time of system.This paper solves this question in terms of the generalized Langevin equation with an Ornstein-Uhlenbeck colored noise. The ergodicity of the momentum variable is studied by using the Khinchin theorem and thus the cost of the momentum correlation function is deepen.

Key words: Brownian motion, momentum correlation function, generalized Langevin equation, ergodicity