Intermittent search process and teleportation

The authors study an intermittent search process combining diffusion and "teleportation" phases in a d -dimensional spherical continuous system and in a regular lattice. The searcher alternates diffusive phases, during which targets can be discovered, and fast phases (teleportation) which randomly relocate the searcher, but do not allow for target detection. The authors show that this alternation can be favorable for minimizing the time of first discovery, and that this time can be optimized by a convenient choice of the mean waiting times of each motion phase. The optimal search strategy is explicitly derived in the continuous case and in the lattice case. Arguments are given to show that much more general intermittent motions do provide optimal search strategies in d dimensions. These results can be useful in the context of heterogeneous catalysis or in various biological examples of transport through membrane pores.