On the spectrums of ergodic Schrodinger operators with finitely valued potentials

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.

arXiv commentThe presentation has been improved. Thank David Damanik for pointing out an error in the statement of Theorem 2 in the earlier version, that C should depend on the potential v. Submitted