Behavior of transport characteristics in several one-dimensional disordered systems

Abstract In this paper we examine the behavior of transport characteristics, such as the mean square displacement, passage times and average flux through a finite segment of the system, in two models of random walks in one-dimensional disordered systems. The first case is the random walk on a regular one-dimensional lattice with asymmetric random hopping probabilities. The second one concerns random motion of particles in a disordered lattice with distance-dependent transfer rates. The main goal of this paper is to answer the question of what are the representative realizations of disorder which support anomalous behavior of transport characteristics. On the basis of such an analysis we recover most of the known results and establish several new ones.