3 years ago

Viscoelastic subdiffusion in random Gaussian potentials.

Igor Goychuk

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in stationary random Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and spatial disorder emerges also naturally. Two type of potential correlations are studied: exponentially-decaying (Ornstein-Uhlenbeck process in space) and algebraically-decaying with an infinite correlation length. It is shown that for a relatively small disorder strength in units of thermal energy (several $k_BT$) viscoelastic subdiffusion in the ensemble sense easily overcomes the potential disorder and asymptotically is not distinguishable from the free-space subdiffusion. However, such subdiffusion on the level of single-tajectory averages still exhibits transiently a characteristic scatter featuring weak ergodicity breaking. With an increase of disorder strength to $5\div 10\; k_BT$, a very long regime of logarithmic Sinai-like diffusion emerges. Long correlations in the potentials fluctuations make such a transient regime essentially longer, but faster in the absolute terms. This nominally ultraslow Sinai diffusion is, however, not dramatically slower than the free-space viscoelastic subdiffusion, in the absolute terms, on the ensemble level. It can transiently be even faster. The explanation of this paradoxical phenomenon is provided. On the level of single-trajectories, such disorder-obstructed persistent viscoelastic subdiffusion is always slower and exhibits a strong scatter in single-trajectory averages.

Publisher URL: http://arxiv.org/abs/1712.05238

DOI: arXiv:1712.05238v2

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