Is subdiffusional transport slower than normal?

Abstract

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale τof strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<τ. However, the transport becomes asymptotically normal for t>>τ. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, <δx(t)> ~ F t^α, <δx^2(t)> ~ t^α, 0<α<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales.