On the Spectrum of the Periodic Anderson-Bernoulli Model

TL;DR

This paper investigates the spectral properties of a periodic Anderson-Bernoulli model using dynamical systems techniques, revealing that the spectrum typically comprises at most four intervals in the case of alternating random potentials.

Contribution

It introduces a novel analysis of the spectrum for a periodic Anderson-Bernoulli model via hyperbolicity of Schrödinger cocycles, providing bounds on the number of spectral intervals.

Findings

Spectrum consists of at most 4 intervals for alternating random potentials

Analysis employs uniform hyperbolicity of Schrödinger cocycles

Provides new insights into spectral structure of periodic Anderson models

Abstract

We analyze the spectrum of a discrete Schrodinger operator with a potential given by a periodic variant of the Anderson Model. In order to do so, we study the uniform hyperbolicity of a Schrodinger cocycle generated by the SL(2,R) transfer matrices. In the specific case of the potential generated by an alternating sequence of random values we show that the almost sure spectrum consists of at most 4 intervals.