Capturing correlations in chaotic diffusion by approximation methods

Abstract

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, whilst the third method approximates Markov partitions and transition matrices by using the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in case of dynamics where exact results for the diffusion coefficient are not available.

11 pages, 5 figures

References in corpus (4)

• Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
• Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases
• Fractal diffusion coefficient from dynamical zeta functions
• Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps

Cited by in corpus (3)

• Dependence of chaotic diffusion on the size and position of holes
• Anti-persistent random walks in time-delayed systems
• Singularity of Levy walks in the lifted Pomeau-Manneville map