Nonequilibrium diffusion induced by a spatio-temporal fluctuation

T. Monnai

Research output: Contribution to journalArticle

Abstract

Spatio-temporal generalization of the Ornstein-Uhlenbeck process has been received considerable attention in the context of coagulations in a random flow. We shall explore the diffusion process with a symmetric spatio-temporal correlated noise in the presence of the external force for the underdamped case. In a nontrivial short correlation limit, the role of spatial correlation is explored and a Fokker-Planck equation is derived based on the stochastic Liouville equation. Our Fokker-Planck equation interpolates the recently proposed diffusion equation describing the generalized Ornstein-Uhlenbeck processes and the traditional Kramers equation. In the small limit of the characteristic value of the momentum given by the mass, spatial and temporal correlation lengths, the diffusion coefficient is proportional to the inverse of the momentum. On the other hand, for the large limit of the characteristic momentum constant, the usual Brownian motion without spatial randomness is reproduced. The analytic form of the steady state distribution is numerically verified with use of the stochastic simulation.

Original languageEnglish
Article numberP01055
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2009
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Ornstein-Uhlenbeck process
Non-equilibrium
Momentum
Spatial Correlation
Fokker-Planck equation
Fluctuations
Fokker-Planck Equation
momentum
Generalized Ornstein-Uhlenbeck Process
Correlated Noise
Liouville Equation
Liouville equations
Steady-state Distribution
Temporal Correlation
Ornstein-Uhlenbeck Process
Coagulation
Stochastic Simulation
Correlation Length
coagulation
Diffusion equation

Keywords

  • Driven diffusive systems (theory)

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistical and Nonlinear Physics
  • Statistics, Probability and Uncertainty

Cite this

Nonequilibrium diffusion induced by a spatio-temporal fluctuation. / Monnai, T.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2009, No. 1, P01055, 2009.

Research output: Contribution to journalArticle

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