Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation

Pavol Kalinay, Jerome Percus

Research output: Contribution to journalArticle

Abstract

A point-like particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the 1D Fokker-Planck (Kramers) equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m → 0, with a series of corrections expanded in powers of m/γ, γ denotes the friction coefficient. The corrections are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.

Original languageEnglish (US)
Pages (from-to)1135-1155
Number of pages21
JournalJournal of Statistical Physics
Volume148
Issue number6
DOIs
StatePublished - Sep 2012

Fingerprint

Fokker-Planck Equation
Phase Space
Smoluchowski Equation
Friction Coefficient
Harmonic Oscillator
Damped
Recurrence
coefficient of friction
harmonic oscillators
Biased
Valid
Denote
Series
Dependent
Model

Keywords

  • Confined diffusion
  • Inertial effects
  • Mapping
  • Smoluchowski equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation. / Kalinay, Pavol; Percus, Jerome.

In: Journal of Statistical Physics, Vol. 148, No. 6, 09.2012, p. 1135-1155.

Research output: Contribution to journalArticle

Kalinay, Pavol ; Percus, Jerome. / Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation. In: Journal of Statistical Physics. 2012 ; Vol. 148, No. 6. pp. 1135-1155.
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