Disordered iterated maps: spectral properties, escape rates and anomalous transport

Abstract

We investigate the transport properties of simple iterated maps with quenched disorder. The dynamics of these systems is mapped to random walks in random environments with next-nearest-neighbour transitions, constituting generalizations of the well-known Sinai model. The non-equilibrium properties are studied numerically by a direct observation of the transport behaviour, by investigating the density of states of the propagator and by considering the system-size dependence of the escape rate. Characteristic exponents associated with each of these quantities are determined and their dependence on the system parameters is evaluated. We find anomalously slow behaviour which in general deviates from the Sinai case and therefore generalizes the latter. These deviations are attributed to the generic absence of detailed balance, which implies that a potential can no longer be assigned.