Fractional Fokker-Planck dynamics: Numerical algorithm and simulations

TL;DR

This paper develops a versatile numerical algorithm to simulate fractional Fokker-Planck dynamics, enabling the study of anomalous transport phenomena in tilted periodic potentials and comparing normal and fractional diffusion behaviors.

Contribution

A novel numerical algorithm for fractional Fokker-Planck equations applicable to arbitrary potentials is introduced and used to analyze fractional transport and diffusion properties.

Findings

The algorithm efficiently simulates fractional dynamics in various potentials.

Fractional current and nonlinear mobility are characterized in washboard potentials.

Differences between normal and fractional diffusion are highlighted through probability density evolution.

Abstract

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.