TY - JOUR

T1 - Susceptibility to disorder of the optimal resetting rate in the Larkin model of directed polymers

AU - Grange, Pascal

N1 - Publisher Copyright:
© 2020 The Author(s). Published by IOP Publishing Ltd.

PY - 2020/9/17

Y1 - 2020/9/17

N2 - 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 r* 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 r* of the resetting rate. We obtain the susceptibility of the optimal resetting rate to disorder in closed form, and find it to be positive.

AB - 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 r* 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 r* of the resetting rate. We obtain the susceptibility of the optimal resetting rate to disorder in closed form, and find it to be positive.

KW - Directed polymers

KW - Random-force model

KW - Stochastic resetting

UR - http://www.scopus.com/inward/record.url?scp=85091760934&partnerID=8YFLogxK

U2 - 10.1088/2399-6528/abb752

DO - 10.1088/2399-6528/abb752

M3 - Article

AN - SCOPUS:85091760934

SN - 2399-6528

VL - 4

SP - 1

EP - 16

JO - Journal of Physics Communications

JF - Journal of Physics Communications

IS - 9

M1 - 095018

ER -