Flashing subdiffusive ratchets in viscoelastic media

Abstract

We study subdiffusive ratchet transport in periodically and randomly flashing potentials. Central Brownian particle is elastically coupled to surrounding auxiliary Brownian quasi-particles which account for the influence of viscoelastic environment. Similar to standard dynamical modeling of Brownian motion, the external force influences only the motion of central particle not affecting directly the environmental degrees of freedom (see video). Just a handful of auxiliary Brownian particles suffice to model subdiffusion over many temporal decades. Time-modulation of the potential violates the symmetry of thermal detailed balance and induces anomalous subdiffusive current which exhibits a remarkable quality at low temperatures, as well as a number of other surprising features such as saturation at low temperatures, and multiple inversions of the transport direction upon a change of the driving frequency in nonadiabatic regime. Our study generalizes classical Brownian motors towards operating in sticky viscoelastic environments like cytosol of biological cells or dense polymer solutions.