Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks
- Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensembleBias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.…
Verfasserangaben: | Takuma Akimoto, Andrey G. CherstvyORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.98.022105 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/30253516 |
Titel des übergeordneten Werks (Englisch): | Physical review : E, Statistical, nonlinear and soft matter physics |
Verlag: | American Physical Society |
Verlagsort: | College Park |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 07.08.2018 |
Erscheinungsjahr: | 2018 |
Datum der Freischaltung: | 18.10.2021 |
Band: | 98 |
Ausgabe: | 2 |
Seitenanzahl: | 6 |
Fördernde Institution: | JSPSMinistry of Education, Culture, Sports, Science and Technology, Japan (MEXT)Japan Society for the Promotion of Science [16KT0021]; DFGGerman Research Foundation (DFG) [ME 1535/6-1, ME 1535/7-1]; Foundation for Polish Science (Humboldt Polish Honorary Research Scholarship) |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer Review: | Referiert |
Publikationsweg: | Open Access / Hybrid Open-Access |
Lizenz (Deutsch): | CC-BY - Namensnennung 4.0 International |