Title
On the spectrum of the critical almost Mathieu operator at rational frequencies
Abstract
The almost Mathieu operator is of fundamental importance in the spectral theory of Schrödinger operators. We present recent joint work with I. Krasovsky and S. Jitomirskaya on deriving a new Chambers-type formula and using it to prove a sharper upper bound for the Lebesgue measure of the spectrum of the critical almost Mathieu operator at rational frequencies. This is a step towards proving a conjecture of Thouless on the asymptotics of the measure of the same spectrum.
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