平方Fibonacci Hamilton算子的混合谱域
Mixed spectral regimes for square Fibonacci Hamiltonians
摘要：
对于平方三对角Fibonacci哈密顿量，我们证明了存在一个开放的参数集，产生混合的区间康托谱（即包含一个区间以及康托尔集的频谱），以及混合的状态密度测量（即一个绝对连续和奇异连续分量都是非零的）。使用本文开发的方法，我们还表明存在的参数制度的平方连续Fibonacci薛定谔算子产生混合区间康托谱。这些例子提供了第一个明确的例子，一个有趣的现象，迄今尚未观察到在非周期哈密顿。此外，虽然我们只关注斐波那契模型，但我们的技术同样适用于基于任何两个字母的原始可逆替换的模型。
英文摘要：
For the square tridiagonal Fibonacci Hamiltonian, we prove existence of an open set of parameters which yield mixed interval-Cantor spectra (i.e. spectra containing an interval as well as a Cantor set), as well as mixed density of states measure (i.e. one whose absolutely continuous and singular continuous components are both nonzero). Using the methods developed in this paper, we also show existence of parameter regimes for the square continuum Fibonacci Schrodinger operator yielding mixed interval-Cantor spectra. These examples provide the first explicit examples of an interesting phenomenon that has not hitherto been observed in aperiodic Hamiltonians. Moreover, while we focus only on the Fibonacci model, our techniques are equally applicable to models based on any two-letter primitive invertible substitution.
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