稀疏CMV矩阵的量子阵发性及其在半直线上量子行走中的应用
Quantum Intermittency for Sparse CMV Matrices with an Application to Quantum Walks on the Half-Line
摘要：
我们研究的动态迭代（半行）CMV矩阵稀疏，高障碍。使用Tcheremchantsev的方法，我们能够显式地计算该模型的输运指数在给定的参数。由于Cantero-Grünbaum-Moral-Velázquez的半线上的CMV矩阵和量子行走之间的联系，我们的结果也允许我们计算对应于稀疏填充强反射体的量子行走的输运指数。据我们所知，这提供了第一个严格的量子行走的例子，它表现出量子不对称性，即，传输指数的不恒定性。当结合CMV版本的Jitomirskaya-Last从属性理论和Damanik-Fillman-Vance的一般离散时间动力学边界时，我们能够精确地计算相关谱测度的Hausdorff维数。
英文摘要：
We study the dynamics given by the iteration of a (half-line) CMV matrix with sparse, high barriers. Using an approach of Tcheremchantsev, we are able to explicitly compute the transport exponents for this model in terms of the given parameters. In light of the connection between CMV matrices and quantum walks on the half-line due to Cantero-Grünbaum-Moral-Velázquez, our result also allows us to compute transport exponents corresponding to a quantum walk which is sparsely populated with strong reflectors. To the best of our knowledge, this provides the first rigorous example of a quantum walk which exhibits quantum intermittency, i.e., nonconstancy of the transport exponents. When combined with the CMV version of the Jitomirskaya-Last theory of subordinacy and the general discrete-time dynamical bounds from Damanik-Fillman-Vance, we are able to exactly compute the Hausdorff dimension of the associated spectral measure.
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