Transport in random networks in a field: interacting particles

Abstract

Transport through a random medium in an external field is modelled by particles performing biased random walks on the infinite cluster above the percolation threshold. Steps are more likely in the direction of the field-say downward-than against. A particle is allowed to move only onto an empty site (particles interact via hard core exclusion). Branches that predominantly point downwards and backbends-backbone segments on which particles must move upwards-act as traps. The authors have studied the movement of interacting random walkers in branches and backbends by Monte Carlo simulations and also analytically. In the full network, the trap-limited current flows primarily through the part of the backbond composed of paths with the smallest backbends and its magnitude in high fields is estimated. Unlike in the absence of interactions, the drift velocity does not vanish in finite fields. However, it continues to show a non-monotonic dependence on the field over a sizeable range of density and percolation probability.