Abstract

We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies.

中文翻译：

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准周期薛定谔 Cocycle 的 Lyapunov 指数的大偏差估计和 Hölder 正则

摘要

我们考虑具有解析势的一维准周期薛定谔算子。在正 Lyapunov 指数方案中，我们证明了大偏差估计，这导致 Lyapunov 指数的 Hölder 连续性和状态的积分密度，在小 Lyapunov 指数和大耦合方案中。我们的结果涵盖了所有丢番图频率和一些刘维尔频率。