Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper’s Model
Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper’s Model
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DOI：
10.1007/s00220-012-1465-4
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发表时间：
2010-10
影响因子：
2.4
通讯作者：
S. Jitomirskaya;C. Marx
中科院分区：
文献类型：
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作者：
S. Jitomirskaya;C. Marx
我们展示了如何扩展（以及有什么限制）阿维拉的全球理论的分析SL（2，C）上循环的家庭的上循环奇点。这使我们能够开发一种策略，以确定扩展的哈珀的模型，所有的参数值和所有的非理性频率的李雅普诺夫指数。特别是，这包括自对偶制度，甚至启发式的结果以前不存在于物理学文献。阿维拉的整体理论的扩展也暗示连续行为的LE上的空间的解析上循环。这包括迄今尚未得到的频率的合理近似值。
We show how to extend (and with what limitations) Avila’s global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper’s model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila’s global theory is also shown to imply continuous behavior of the LE on the space of analytic-cocycles. This includes rational approximation of the frequency, which so far has not been available.