The Dry Ten Martini Problem for Sturmian Hamiltonians

2024/02/26 by Band, Ram, Beckus, Siegfried, Loewy, Raphael · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2402.16703

Abstract

The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schrödinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics.

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