Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials
- We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.
Author details: | Tobias GuggenbergerORCiDGND, Aleksei ChechkinORCiDGND, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/ac7b3c |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics |
Publisher: | Dt. Physikalische Ges. |
Place of publishing: | [Bad Honnef] |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/07/07 |
Publication year: | 2022 |
Release date: | 2024/01/12 |
Tag: | Boltzmann distribution; diffusion; fractional Brownian motion |
Volume: | 24 |
Issue: | 7 |
Article number: | 073006 |
Number of pages: | 18 |
Funding institution: | German Science Foundation (DFG) [ME 1535/12-1]; Polish National Agency; for Academic Exchange (NAWA); German Research Foundation (DFG); [491466077] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | CC-BY - Namensnennung 4.0 International |