Diffusion and Localization of Waves in a Time-Varying Random Environment

We investigate the diffusion properties of a quantum particle or wave in a time-evolving random environment. We argue that the problem is equivalent to a classical random walk among traps with a release time distribution given by the time correlation function of the disorder. For a slowly decaying correlation function, we exhibit a new form of localization, characterized by a zero diffusion constant but a nonzero probability of escaping from any region of space. When the correlation time is finite, we argue that, for intermediate disorder, the diffusion constant of the particle will be of the same order of magnitude as the diffusion constant of the impurities.