A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles

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Abstract

We provide a connection between Brownian motion and a classical mechanical system. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random mechanical principles, via interaction potentials, without any assumption requiring that the initial velocities of the environmental particles should be restricted to be “fast enough”. We prove the convergence of the (position, velocity)-process of the massive particle under a certain scaling limit, such that the mass of the environmental particles converges to 0 while the density and the velocities of them go to infinity, and give the precise expression of the limiting process, a diffusion process.

Original languageEnglish
Pages (from-to)286-350
Number of pages65
JournalJournal of Statistical Physics
Volume170
Issue number2
DOIs
Publication statusPublished - 2018 Jan 1
Externally publishedYes

Keywords

  • Brownian motion
  • Classical mechanics
  • Convergence
  • Diffusion
  • Infinite particle systems
  • Markov processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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