Localization transition of a resetting random walk induced by multiple impurities.

Abstract

We study the problem of a resetting random walk on a lattice in the presence of impurities, and, as has been previously shown with a single impurity, the walker undergoes a transition from a localized to delocalized state. We study the nature of the localized states and transition to delocalized state in the presence of two impurities. We find that when the separation between impurities exceeds a characteristic length, the stronger impurity determines the transition threshold and the walker becomes localized on the stronger impurity. Deviation from the single-impurity phase diagram occurs when the impurities are close to each other and have almost the same strength, and the transition threshold is less than the threshold of each of impurities. In other words, two impurities enhance the localization.