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Spectral gaps of the Schrödinger operators with periodic δ′-interactions and Diophantine approximations
Published online by Cambridge University Press: 01 July 2007
Abstract
We study the spectral gaps of the Schrödinger operatorwhere κ∈(0,2π) and are parameters. Let τ=2π−κ. Suppose that the ratio κ0:=τ/κ is irrational. We denote the jth gap of the spectrum of H by Gj, its length by |Gj|. We obtain a relationship between the asymptotic behaviour of |Gj| as j→∞ and the Diophantine properties of κ0. In particular, we show that if β1+β2=0, thenwhere M(κ0) stands for the Markov constant of κ0.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 185 - 199
- Copyright
- Copyright © Cambridge Philosophical Society 2007
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