  Viscoelastic subdiffusion governed by a fractional Langevin equation is
studied numerically in a random Gaussian environment modeled by stationary
Gaussian potentials with decaying spatial correlations. This anomalous
diffusion is archetypal for living cells, where cytoplasm is known to be
viscoelastic and a spatial disorder also naturally emerges. We obtain some
first important insights into it within a model one-dimensional study. Two
basic types of potential correlations are studied: short-range exponentially
decaying and algebraically slow decaying with an infinite correlation length,
both for a moderate (several $k_BT$, in the units of thermal energy), and
strong (5-10 $k_BT$) disorder. For a moderate disorder, it is shown that on the
ensemble level viscoelastic subdiffusion can easily overcome the medium's
disorder. Asymptotically, it is not distinguishable from the disorder-free
subdiffusion. However, a strong scatter in single-trajectory averages is
nevertheless seen even for a moderate disorder. It features a weak ergodicity
breaking, which occurs on a very long yet transient time scale. Furthermore,
for a strong disorder, a very long transient regime of logarithmic, Sinai-type
diffusion emerges. It can last longer and be faster in the absolute terms for
weakly decaying correlations as compare with the short-range correlations.
Residence time distributions in a finite spatial domain are of a generalized
log-normal type and are reminiscent also of a stretched exponential
distribution. They can be easily confused for power-law distributions in view
of the observed weak ergodicity breaking. This suggests a revision of some
experimental data and their interpretation.
