LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

Satya Majumdar

LPTMS, Orsay

We study a simple model of search where the searcher undergoes normal diffusion, but once in a while resets to its initial starting point stochastically with rate $r$. The effect of a finite resetting rate r turns out to be rather drastic. First, the position of the walker approaches a nonequilibrium stationary state at long times. The approach to the stationary state is accompanied by an interesting `dynamical' phase transition. For searching an immobile target, resetting leads to finite mean search time which, as a function of r, has a minimum at an optimal resetting rate $r^*$. This makes the search process efficient. We then consider various generalizations of this simple resetting model: to Levy flights, to multiple walkers and also to spatially extended system such as fluctuating interfaces.