高阶动力学粒子的布朗运动

涂展春

doi:10.12202/j.0476-0301.2023187

高阶动力学粒子的布朗运动

doi: 10.12202/j.0476-0301.2023187

涂展春

北京师范大学物理学系，100875，北京

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出版历程
- 录用日期: 2023-03-01
- 网络出版日期: 2023-11-18

Brownian motion with high-derivative dynamics

TU Zhanchun

Department of Physics，Beijing Normal University，Beijing 100875，China

摘要

摘要: 讨论了与谐振子热浴耦合的高阶动力学粒子的运动行为，导出了含高阶动力学的朗之万方程及其对应的福克-普朗克方程．
- 高阶动力学 /
- 布朗运动 /
- 朗之万方程 /
- 福克-普朗克方程
Abstract: In this paper, Brownian motion with higher-derivative dynamics is investigated. As a model, we consider a particle coupling with a heat bath consisting of harmonic oscillators. Assume that the motion of the particle without the bath is determined by a Lagrangian $ L = L\left(t,x,{x}_{1},\cdots ,{x}_{N}\right) $ where $ {x}_{n} $ (n = $1, 2, \cdots $, N) is the n-th order derivative of x with respect to time t. After integrating the variables of bath, we derived a generalized Langevin equation for Brownian motion:
- high-derivative dynamics /
- Brownian motion /
- Langevin equation /
- Fokker-Planck equation

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参考文献(30)

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