位错常微分方程中的边缘态
Edge states in ordinary differential equations for dislocations
摘要：
在这篇文章中，我们研究薛定谔算子的实线上，当外部势代表一个位错在一个周期性介质。我们研究了谱随位错参数的变化。我们介绍了几个整数值指数，包括陈数的散装指数，和各种谱流的边缘指数。我们证明，所有这些指数相吻合，提供了一个证明散装边缘对应在这种情况下。本文还对狄拉克模型中的位错作了研究。我们证明了0总是这样的运营商的特征值。
英文摘要：
In this article, we study Schrödinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with the dislocation parameter. We introduce several integer-valued indices, including Chern number for bulk indices, and various spectral flows for edge indices. We prove that all these indices coincide, providing a proof a bulk-edge correspondence in this case. The study is also made for dislocations in Dirac models on the real line. We prove that 0 is always an eigenvalue of such operators.
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