First passage time problems and resonant behavior on a fluctuating lattice

We study the mean residence time of a random walker on a line segment of a lattice, which randomly switches between two states. In each of the states only motions in a one way direction are allowed. When the particle can leave the line segment through both of its ends, the residence time is a monotonous increasing function of the switching rate and does not depend on the initial state of the lattice. Nevertheless, if one of the boundaries of the segment is reflecting, it goes through a minimum for a given value of the flipping rate, showing a resonancelike behavior. The results are compared with previous studies of first passage time problems in time-dependent fields.