Random search with stochastic resetting: When finding the target is not enough

In this paper, we consider a random search process with stochastic resetting and a partially accessible target U. In contrast to standard search processes, we assume that when the searcher first finds the target by contacting the surface ∂U, it does not have immediate access to the resources within the target interior. Instead, it spends a random waiting time attached to the surface, after which it either gains access to the resources or detaches and continues its search process. We also assume that the searcher requires an alternating sequence of periods of bulk diffusion interspersed with local surface interactions before being able to attach to the surface. The attachment, detachment, and target entry events are the analogs of adsorption, desorption, and absorption of a particle by a partially reactive surface in physical chemistry. Using renewal theory, we analytically derive the nonequilibrium stationary state and mean first passage time statistics for several configurations, including both the half-line and higher-dimensional geometries, and models incorporating non-Markovian absorption.