Stochastic harmonic trapping of a Lévy walk
- We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations areWe introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.…
Author details: | Pengbo Xu, Tian Zhou, Ralf MetzlerORCiDGND, Weihua DengORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/ac5282 |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics |
Subtitle (English): | transport and first-passage dynamics under soft resetting strategies |
Publisher: | Deutsche Physikalische Gesellschaft |
Place of publishing: | Bad Honnef |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/03/08 |
Publication year: | 2022 |
Release date: | 2022/09/13 |
Tag: | Levy walks; anomalous diffusion; diffusion; stochastic resetting |
Volume: | 24 |
Issue: | 3 |
Article number: | 033003 |
Number of pages: | 28 |
First page: | 1 |
Last Page: | 28 |
Funding institution: | National Natural Science Foundation of China [12071195] |
Funding institution: | AI and Big Data; Funds [2019620005000775] |
Funding institution: | German Science Foundation (DFG) [ME; 1535/12-1] |
Funding institution: | Fundacja na rzecz Nauki; Polskiej, FNP |
Funding institution: | China Postdoctoral Science Foundation [8206300491] |
Funding institution: | German Research Foundation |
Funding institution: | Potsdam University |
Funding number: | 12071195 |
Funding number: | 2019620005000775 |
Funding number: | ME; 1535/12-1 |
Funding number: | 8206300491 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Extern / Extern | |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Grantor: | Publikationsfonds der Universität Potsdam |
Publishing method: | Open Access / Gold Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1262 |