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Correlated continuous-time random walks in external force fields

  • We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T-i is equal to the previous waiting time Ti-1 plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.

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Author:Marcin Magdziarz, Ralf MetzlerORCiDGND, Wladyslaw Szczotka, Piotr Zebrowski
ISSN:1539-3755 (print)
ISSN:1550-2376 (online)
Parent Title (English):Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert