Superstatistical generalised Langevin equation
- Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellentRecent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.…
Author details: | Jakub ŚlęzakORCiD, Ralf MetzlerORCiDGND, Marcin Magdziarz |
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URN: | urn:nbn:de:kobv:517-opus4-409315 |
Subtitle (English): | non-Gaussian viscoelastic anomalous diffusion |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (413) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2018/03/28 |
Publication year: | 2018 |
Publishing institution: | Universität Potsdam |
Release date: | 2018/03/28 |
Tag: | anomalous diffusion; generalised langevin equation; non-Gaussian diffusion; superstatistics |
Number of pages: | 25 |
Source: | New Journal of Physics 20 (2018) Nr. 023026, S. 1–25 DOI: 10.1088/1367-2630/aaa3d4 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access |
License (English): | Creative Commons - Namensnennung 3.0 Unported |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |