Statistical Properties of Disordered Driven Lattice Gases with Open Boundaries

Summary

We investigate driven lattice gases with open boundary conditions in presence of randomly distributed defect sites with reduced hopping rate 1. These systems can be used as models for intracellular transport systems impurified by immobile blocking molecules. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We show that the leading behaviour in the disordered system is determined by the longest stretch of consecutive defect sites. Using results from extreme value statistics 2 this single-bottleneck approximation gives accurate results for the expectation values of the maximum current at small defect densities. Corrections from bottleneck interactions can be taken into account systematically by a perturbative expansion.