Anomalous Mobility Enhancement in Restricted Geometries

Abstract

We investigate the effect of geometrical confinement on driven transport in anomalous media within the framework of the quenched trap model. The particle performs a biased random walk on a lattice, where quenched disorder introduces power-law distributed trapping times. We consider channels that are infinite along one direction and have a finite cross-section in the remaining $d-1$ directions. In the glassy regime, where $α=T/T_g<1$, we derive an analytical expression for the mean longitudinal displacement in the long-time and weak-force limits. We find the scaling $\langle x_\parallel(t)\rangle \propto F_\parallel^αt^αΩ^{-(1-α)}$, where $F_\parallel>0$ is the effective longitudinal force and $Ω$ is the number of sites in a transverse cross-section. Thus, the anomalous mobility is enhanced for narrower channels. Our analytical result applies to general Bravais lattices in $d$ dimensions with periodic transverse boundary conditions. Numerical simulations confirm the analytical predictions for different lattice geometries and show quantitative agreement even for channels with reflecting boundary conditions.