Diffusive scaling for all moments of the Markov Anderson model

TL;DR

This paper establishes diffusive scaling for all moments of the wave amplitude in a Markovian disordered quantum system, providing a uniform bound on exponential moments and a comprehensive central limit theorem.

Contribution

It extends previous results by proving diffusive behavior for all moments and obtaining uniform exponential bounds in a Markov noise setting.

Findings

Proved diffusive scaling for all moments of the wave amplitude.

Established a uniform bound on exponential moments.

Derived a central limit theorem for the model.

Abstract

We consider a tight-binding Schroedinger equation with time dependent diagonal noise, given as a function of a Markov process. This model was considered previously by Kang and Schenker (J. Stat. Phys., 134(5-6):1005, arXiv:0808.2784), 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.