Abstract
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent α(t) in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by α(t). We derive the essential statistical properties of MMFBM such as its response function, mean-squared displacement (MSD), autocovariance function, and Gaussian distribution. In contrast to existing forms of FBM with time-varying memory exponents but a reset memory structure, the instantaneous dynamic of MMFBM is influenced by the process history, e.g., we show that after a steplike change of α(t) the scaling exponent of the MSD after the α step may be determined by the value of α(t) before the change. MMFBM is a versatile and useful process for correlated physical systems with nonequilibrium initial conditions in a changing environment.
Recommended Citation
W. Wang et al., "Memory-multi-fractional Brownian Motion With Continuous Correlations," Physical Review Research, vol. 5, no. 3, article no. L032025, American Physical Society, Jul 2023.
The definitive version is available at https://doi.org/10.1103/PhysRevResearch.5.L032025
Department(s)
Physics
Publication Status
Open Access
International Standard Serial Number (ISSN)
2643-1564
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2023 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jul 2023
Comments
Deutsche Forschungsgemeinschaft, Grant 2112862/STAXS