Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher's equation, anomalous crossovers and resetting
- We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher's equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher's process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher's process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analyzed in terms of the largeWe analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher's equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher's process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher's process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analyzed in terms of the large deviation function.…
Author details: | Trifce SandevORCiDGND, Ljupco KocarevORCiD, Ralf MetzlerORCiDGND, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.1016/j.chaos.2022.112878 |
ISSN: | 0960-0779 |
ISSN: | 1873-2887 |
Title of parent work (English): | Chaos, solitons & fractals |
Publisher: | Elsevier |
Place of publishing: | Oxford |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/11/16 |
Publication year: | 2022 |
Release date: | 2024/09/26 |
Tag: | Anomalous; Dichotomic noise; Heterogeneous telegrapher's process; Stochastic resetting; diffusion |
Volume: | 165 |
Issue: | 2 |
Article number: | 112878 |
Number of pages: | 11 |
Funding institution: | Alexander von Humboldt Foundation, Germany; Polish National Agency for; Academic Exchange (NAWA); German Science Foundation (DFG) [ME; 1535/12-1]; bilateral Macedonian-Chinese research project under the; intergovernmental Macedonian-Chinese agreement [20-6333] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |
License (German): | Keine öffentliche Lizenz: Unter Urheberrechtsschutz |