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Continuity of the measure of the spectrum for discrete quasiperiodic operators | | S. Ya. Jitomirskaya
; I. V. Krasovsky
; | | Date: |
8 Jul 2001 | | Journal: | Math.Res.Lett. 9 (2002) 413-422 | | Subject: | Spectral Theory; Mathematical Physics | math.SP math-ph math.MP | | Abstract: | We study discrete Schroedinger operators $(H_{alpha, heta}psi)(n)= psi(n-1)+psi(n+1)+f(alpha n+ heta)psi(n)$ on $l^2(Z)$, where $f(x)$ is a real analytic periodic function of period 1. We prove a general theorem relating the measure of the spectrum of $H_{alpha, heta}$ to the measures of the spectra of its canonical rational approximants under the condition that the Lyapunov exponents of $H_{alpha, heta}$ are positive. For the almost Mathieu operator ($f(x)=2lambdacos 2pi x$) it follows that the measure of the spectrum is equal to $4|1-|lambda||$ for all real $ heta$, $lambda
epm 1$, and all irrational $alpha$. | | Source: | arXiv, math.SP/0107061 | | Services: | Forum | Review | PDF | Favorites | |
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