Brownian Motion of a Rayleigh Particle Confined in a Channel: A Generalized Langevin Equation Approach

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• 作者：Changho Kim (1)
  George Em Karniadakis (1)
  
  1. Division of Applied Mathematics ; Brown University ; Providence ; RI ; 02912 ; USA
  
• 关键词：Memory effects ; Long ; time tail ; Finite ; mass effects ; Anomalous diffusion ; Molecular dynamics
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：158
• 期：5
• 页码：1100-1125
• 全文大小：914 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We study confined Brownian motion by investigating the memory function of a \(d\) -dimensional hypercube ( \(d\ge 2\) ), which is subject to a harmonic potential and suspended in an ideal gas confined by two parallel walls. For elastic walls and under the infinite-mass limit, we obtain analytic expressions for the force autocorrelation function and the memory function. The transverse-direction memory function possesses a nonnegative tail decaying like \(t^{-(d-1)}\) , from which anomalous diffusion is expected for \(d=2\) . For \(d=3\) , the position-dependent friction coefficient becomes larger than the unconfined case and the increment is inversely proportional to the square of the distance from the wall. We also perform molecular dynamics simulations with thermal walls and/or a finite-mass hypercube. We observe faster decay due to the thermal wall ( \(t^{-3}\) for \(d=2\) and \(t^{-5}\) for \(d=3\) under the fully thermalizing wall) and convergence behaviors of the finite-mass memory function, which are different from the unconfined case.