Non-Brownian dynamics of biased viscoelastic diffusion in Gaussian random environments

Field-driven particle diffusion in heterogeneous viscoelastic environments is a ubiquitous process in biological systems such as cell cytoplasm. In this paper, we study the behavior of statistical characteristics of a biased fractional Brownian motion (FBM) in spatially correlated Gaussian-disordered landscapes. We numerically investigate the effects of constant drift, the characteristic length of spatial variations, and the root mean squared amplitude of the potential fluctuations on the behavior of the mean squared displacements, kurtosis, velocity autocorrelation function (VAF), and sample p-variation parameters. Our analysis shows that the dynamics for subdiffusive FBM are very sensitive to the external force field. In particular, non-ergodic crossover from a slow diffusion regime to a superdiffusion regime with non-Gaussian behavior arises. However, the effect of bias diminishes with increasing anomalous exponent for FBM. We find that the VAF and sample p-variation can be considered as a possible test to distinguish between subdiffusive FBM in Gaussian disorder landscapes with a spatial correlation and CTRW which somewhat share similar behavior such as anomalous subdiffusion and non-Gaussianity.