Stochastic search with Poisson and deterministic resetting

We investigate a stochastic search process in one, two, and three dimensions in which N di. using searchers that all start at x(0) seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate r, or deterministically, with a reset time T. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for suffciently large N, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for N searchers, including the search time being independent of T for 1/T -> 0 and the search cost being independent of N over a suitable range of N. Moreover, deterministic resetting typically leads to a lower search cost than in Poisson resetting.