Work

Effective diffusion constant of stochastic processes with spatially periodic noise

Year: 2024

Type: article

Abstract: We discuss the effective diffusion constant D_{eff} for stochastic processes with spatially dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived depending on the choice of the discretization rule 0≤α≤1. We initially study the case of periodic heterogeneous diffusion without drift, and we determine a general result for the effective diffusion coefficient D_{eff}, which is valid for any value of α. We study the case of periodic sinusoidal diffusion in detail, and we find a relationship with Legendre functions. Then we derive D_{eff} for general α in the case of diffusion with periodic spatial noise and in the presence of a drift term, generalizing the Lifson-Jackson theorem. Our results are illustrated by analytical and numerical calculations on generic periodic choices for drift and diffusion terms.

Source: Physical review. E

DOI: 10.1103/physreve.110.044123

Authors: Stefano Giordano, Ralf Blossey

Institutions: Institut d'Electronique, de Microélectronique et de Nanotechnologie, Université Polytechnique Hauts-de-France, Université de Lille

Language: English

Topic: stochastic dynamics and bifurcation

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Dynamics of DNA repair proteins at nucleosomes