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.
| Author details: | Marcin Magdziarz, Ralf MetzlerORCiDGND, Wladyslaw Szczotka, Piotr Zebrowski |
|---|---|
| DOI: | https://doi.org/10.1103/PhysRevE.85.051103 |
| ISSN: | 1539-3755 |
| ISSN: | 1550-2376 |
| Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
| Publisher: | American Physical Society |
| Place of publishing: | College Park |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2012 |
| Publication year: | 2012 |
| Release date: | 2017/03/26 |
| Volume: | 85 |
| Issue: | 5 |
| Number of pages: | 5 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
