Fractional Brownian motion with random diffusivity
- Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine aNumerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.…
Author details: | Wei WangORCiD, Andrey G. CherstvyORCiDGND, Aleksei ChechkinORCiDGND, Samudrajit ThapaORCiDGND, Flavio SenoORCiD, Xianbin Liu, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1088/1751-8121/aba467 |
ISSN: | 1751-8113 |
ISSN: | 1751-8121 |
Title of parent work (English): | Journal of physics : A, Mathematical and theoretical |
Subtitle (English): | emerging residual nonergodicity below the correlation time |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/11/04 |
Publication year: | 2020 |
Release date: | 2023/01/09 |
Tag: | anomalous diffusion; diffusing diffusivity; fractional Brownian motion; stochastic processes; weak ergodicity breaking |
Volume: | 53 |
Issue: | 47 |
Article number: | 474001 |
Number of pages: | 34 |
Funding institution: | Chinese Council Scholarship [201806830031]; Deutscher Akademischer; Austauschdienst (DAAD)Deutscher Akademischer Austausch Dienst (DAAD); [57214224]; National Natural Science Foundation of China (NNSFC)National; Natural Science Foundation of China (NSFC) [11472126, 11232007]; Priority Academic Programme Development of Jiangsu Higher Education; Institutions (PAPD); Deutsche Forschungsgemeinschaft (DFG)German; Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science; (Fundacja na rzecz Nauki Polskiej); Alexander von Humboldt Polish; Honorary Research Scholarship; Department of Physics and Astronomy of; Padua University [191017] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 52 Astronomie / 520 Astronomie und zugeordnete Wissenschaften |
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik | |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |