Susceptibility to disorder of the optimal resetting rate in the Larkin model of directed polymers

Abstract

Abstract We consider the Larkin model of a directed polymer with Gaussian-distributed random forces, with the addition of a resetting process whereby the transverse position of the end-point of the polymer is reset to zero with constant rate r. We express the average over disorder of the mean time to absorption by an absorbing target at a fixed value of the transverse position. Thanks to the independence properties of the distribution of the random forces, this expression is analogous to the mean time to absorption for a diffusive particle under resetting, which possesses a single minimum at an optimal value of the resetting rate . Moreover, the mean time to absorption can be expanded as a power series of the amplitude of the disorder, around the value of the resetting rate. We obtain the susceptibility of the optimal resetting rate to disorder in closed form, and find it to be positive.