Persistence effects in deterministic diffusion

Abstract

In systems which 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.

7 pages, 7 figures

References in corpus (4)

• Heat conduction and Fourier's law by consecutive local mixing and thermalization
• Understanding deterministic diffusion by correlated random walks
• Heat conductivity from molecular chaos hypothesis in locally confined billiard systems
• Random walk approach to the d-dimensional disordered Lorentz gas

Cited by in corpus (11)

• Normal and Anomalous Diffusion in Soft Lorentz Gases
• Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards
• Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases
• Diffusion coefficients for multi-step persistent random walks on lattices
• Anti-persistent random walks in time-delayed systems
• An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas
• A two-stage approach to relaxation in billiard systems of locally confined hard spheres
• Capturing correlations in chaotic diffusion by approximation methods
• Anomalous Diffusion in the Square Soft Lorentz Gas
• Efficient algorithms for general periodic Lorentz gases in two and three dimensions
• Diffusion in the Inverted Triangular Soft Lorentz Gas