Search of stochastically gated targets with diffusive particles under resetting

Abstract

The effects of Poissonian resetting at a constant rate r on the reaction time between a Brownian particle and a stochastically gated target are studied. The target switches between a reactive state and a non-reactive one. We calculate the mean time at which the particle subject to resetting hits the target for the first time, while the latter is in the reactive state. The search time is minimum at a resetting rate that depends on the target transition rates. When the target relaxation rate is much larger than both the resetting rate and the inverse diffusion time, the system becomes equivalent to a partially absorbing boundary problem. In other cases, however, the optimal resetting rate can be a non-monotonic function of the target rates, a feature not observed in partial absorption. We compute the relative fluctuations of the first hitting time around its mean and compare our results with the ungated case. The usual universal behavior of these fluctuations for resetting processes at their optimum breaks down due to the target internal dynamics.

Gated reactions in discrete time and space

“…Relating gated reaction times to their ungated counterparts, the framework developed herein extends our knowledge on the long studied topic of first-passage. Importantly, all the results obtained apply beyond the context of chemical reactions and could e.g., be used to analyze analogous scenarios which arise when considering search of stochastically gated targets [27,28] and to the problem of first-detection with intermittent sensing [17].…”

“…Mercado-Vásquez and Boyer studied the reaction time of a gated 1D diffusing particle on the semi-infinite line [26], adding novel insights to the works of Budde, Cáceres and Ré [11][12][13]. They then proceeded to extend their theory to the cases of a gated run-and-tumble particle [27] and a gated diffusive particle under restart [28]. The latter was also previously considered by Bressloff with a slightly different model [29].…”