Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces

TL;DR

This paper explores how external forces influence anomalous diffusion using Langevin equations, introducing biasing and decoupled force models, and deriving new formulations for time-dependent force fields.

Contribution

It introduces the concepts of biasing and decoupled external fields in Langevin equations for anomalous diffusion and derives a new formulation for decoupled time-dependent force fields.

Findings

Different models for external forces in anomalous diffusion are discussed.

A Langevin formulation for decoupled time-dependent force-fields is derived.

The approach extends previous models to include decoupled external influences.

Abstract

The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it biasing} and {\it decoupled} external fields is introduced. Complementary to the recently established Langevin equations for anomalous diffusion in a time-dependent external force-field [{\it Magdziarz et al., Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of anomalous diffusion in a decoupled time-dependent force-field is derived.