Viscoelastic subdiffusion in random Gaussian potentials*

Subdiffusion in a fluctuating environment is archetypal for viscoelastic cytosol of living cells, where a spatial disorder also naturally emerges. We model it by a generalized Langevin equation dynamics with long-range memory in stationary random Gaussian potentials featured by decaying spatial correlations. It is shown that for a relatively small potential energy disorder in units of thermal energy (several k_BT) viscoelastic subdiffusion in the ensemble sense easily overcomes the potential disorder. Asymptotically it is not distinguishable from the unobstructed subdiffusion. However, diffusion on the level of single-trajectory averages still exhibits transiently a characteristic scatter featuring weak ergodicity breaking. With an increase of the disorder strength to 5-10 k_BT, a very long transient regime of logarithmic or Sinai-like diffusion emerges. This nominally ultraslow Sinai diffusion can, however, be transiently even faster than the free-space viscoelastic subdiffusion, in the absolute terms, on the ensemble level. On the level of single-trajectories, such a strongly obstructed viscoelastic subdiffusion is always slower and exhibits a strong scatter in single-trajectory averages.