Persistence effects in deterministic diffusion

Thomas Gilbert and David P. Sanders
Phys. Rev. E 80, 041121 – Published 16 October 2009

Abstract

In systems that exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random-walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of “persistence” on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.

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  • Received 5 August 2009

DOI:https://doi.org/10.1103/PhysRevE.80.041121

©2009 American Physical Society

Authors & Affiliations

Thomas Gilbert1,* and David P. Sanders2,†

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
  • 2Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México D.F., Mexico

  • *thomas.gilbert@ulb.ac.be
  • dps@fciencias.unam.mx;http://sistemas.fciencias.unam.mx/~dsanders

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Vol. 80, Iss. 4 — October 2009

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