| Abstract: |
| For periodic Schr\odinger operators $H_{v,\alpha,x}$ with analytic potentials and frequency $\alpha\in \mathbb{Q}$. Let $S_-$ be the intersection of the spectra over all phases $x$. We show that $S_-(\alpha)$ is the limit of $S_-(p/q)$ for a class of rational approximations $p/q \to \alpha$, except possibly on a set of Lebesgue measure zero. This settles a question originally raised by S. Jitomirskaya. This is a joint work with S. Jitomirskaya and L. Shao. |
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