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We consider a tight-binding Schroedinger equation with time dependentdiagonal noise, given as a function of a Markov process. This model wasconsidered previously by Kang and Schenker (J. Stat. Phys., 134(5-6):1005,arXiv:0808.2784), who proved that the wave propagates diffusively. We revisitthe proof of diffusion so as to obtain a uniform bound on exponential momentsof the wave amplitude and a central limit theorem that implies, in particular,diffusive scaling for all position moments of the mean wave amplitude.

Diffusive scaling for all moments of the Markov Anderson model