Aging Scaled Brownian Motion

Abstract

Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly non-stationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form, that is identical to the aging behavior of scale free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly non-ergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.

10 pages, 8 figures, REVTeX

References in corpus (5)

• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
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Cited by in corpus (4)

• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
• Langevin formulation of a subdiffusive continuous time random walk in physical time
• Ultraslow scaled Brownian motion
• Ergodicity breaking, ageing, and confinement in generalised diffusion processes with position and time dependent diffusivity