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Condensed Matter > Statistical Mechanics
Title: Memory-multi-fractional Brownian motion with continuous correlations
(Submitted on 2 Mar 2023 (v1), last revised 3 Aug 2023 (this version, v2))
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 $\alpha(t)$ in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by $\alpha(t)$. We derive the essential statistical properties of MMFBM such as response function, mean-squared displacement (MSD), autocovariance function, and Gaussian distribution. In contrast to existing forms of FBM with time-varying memory exponents but reset memory structure, the instantaneous dynamic of MMFBM is influenced by the process history, e.g., we show that after a step-like change of $\alpha(t)$ the scaling exponent of the MSD after the $\alpha$-step may be determined by the value of $\alpha(t)$ before the change. MMFBM is a versatile and useful process for correlated physical systems with non-equilibrium initial conditions in a changing environment.
Submission history
From: Ralf Metzler [view email][v1] Thu, 2 Mar 2023 19:50:03 GMT (379kb)
[v2] Thu, 3 Aug 2023 07:14:02 GMT (547kb)
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