Diffusive Scaling for All Moments of the Markov Anderson Model

#### C. Musselman, J. Schenker

2015, v.21, №3, 751-778

ABSTRACT

We consider a tight-binding Schr\"odinger equation with time dependent diagonal noise, given as a function of a Markov process. This model was considered previously by Kang and Schenker \cite{Kang2009b}, who proved that the wave propagates diffusively. We revisit the proof of diffusion so as to obtain a uniform bound on exponential moments of the wave amplitude and a central limit theorem that implies, in particular, diffusive scaling for all position moments of the mean wave amplitude.
Some of the results presented here appeared in the Ph.D.\
thesis of the first author .

Keywords: diffusion, Markov processes, wave propagation, random Schr\"odinger equation