1st passage times and transport in systems with disorder

Abstract

We illustrate how first passage times can be calculated in systems with disorder. We use a renormalization approach to discuss first passage times in one-dimensional continuous time random walks and deterministic fractals. We discuss the phenomenon of field-induced trapping on a random comb. Finally, we calculate mean first-passage times for one-dimensional random walks, and discuss, in particular, the case of Sinai disorder. In a short Appendix, we show how mean first-passage times can be calculated for an arbitrary inhomogeneous continuous time random walk in one dimension, using a recursion relation similar in spirit to the renormalization approach.