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- W2519855114 abstract "We consider the spectrum of the almost Mathieu operator $H_alpha$ with frequency $alpha$ and in the case of the critical coupling. Let an irrational $alpha$ be such that $|alpha-p_n/q_n|<c q_n^{-varkappa}$, where $p_n/q_n$, $n=1,2,dots$ are the convergents to $alpha$, and $c$, $varkappa$ are positive absolute constants, $varkappa<56$. Assuming certain conditions on the parity of the coefficients of the continued fraction of $alpha$, we show that the central gaps of $H_{p_n/q_n}$, $n=1,2,dots$, are inherited as spectral gaps of $H_alpha$ of length at least $c'q_n^{-varkappa/2}$, $c'>0$." @default.
- W2519855114 created "2016-09-23" @default.
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- W2519855114 date "2016-10-20" @default.
- W2519855114 modified "2023-09-23" @default.
- W2519855114 title "Central Spectral Gaps of the Almost Mathieu Operator" @default.
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- W2519855114 doi "https://doi.org/10.1007/s00220-016-2774-9" @default.
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