Anomalous non-Gaussian diffusion of scaled Brownian motion in a quenched disorder environment

Abstract

Abstract This paper aims to investigate particle dynamics in a random environment, subjected to power-law time-dependent temperature. To this end, the scaled Brownian motion (SBM), a stochastic process described by a diffusion equation with time-dependent diffusivity, has been studied numerically in quenched disordered systems (QDLs). Here, QDLs have been modeled by spatial correlated Gaussian random potential with an exponential normalized correlation function. Results show nonergodic non-Gaussian subdiffusion for subdiffusive SBM. While a crossover from non-Gaussian Brownian diffusion to long-time Gaussian superdiffusion has been observed for the superdiffusive SBM scenario. Furthermore, the first passage time to an object significantly depends on the governing SBM regime and its scale parameter, where the first passage time becomes faster with the increasing scale parameter. The mechanism underlying these behaviors has been uncovered numerically.