On the spectrums of ergodic Schrodinger operators with finitely valued potentials

2015/02/09 by Zhiyuan Zhang, Zhang, Zhiyuan
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1502.02317

openalex publication_date 2015/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the measure of the spectrum of Schrödinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the coupling constant tends to infinity. We also obtained a quantitative upper bound for the measure of the spectrum. This follows from a result we proved for ergodic Schrödinger operators with finitely valued potentials under two conditions on the recurrence property of the shift. We also show that one of these conditions is necessary for such result.

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