论文标题
部分可观测时空混沌系统的无模型预测
An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
论文作者
论文摘要
在本文中，我们讨论了Toeplitz运算符的索引理论，该索引理论是在两种可变性有理矩阵函数符号的离散四分之一平面上讨论的。通过将Gohberg-Krein理论用于矩阵因素化，我们将最初定义在二维圆环定义的符号扩展到某些三维球体，并得出一个公式，以通过扩展符号来表达其Fredholm索引。还包括（自我偶像）弗雷德·四分之一平面Toeplitz运营商和保留真实结构的家族的变体。对于某些散装边缘的单粒子汉密尔顿汉密尔顿人有限跳跃范围的单粒子汉密尔顿人，在带有codimension-two直角角的离散晶格上，与角状态有关的拓扑不变性是通过散装汉密尔顿人的扩展提供的。
In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on a two-dimensional torus to some three-dimensional sphere and derive a formula to express their Fredholm indices through extended symbols. Variants for families of (self-adjoint) Fredholm quarter-plane Toeplitz operators and those preserving real structures are also included. For some bulk-edge gapped single-particle Hamiltonians of finite hopping range on a discrete lattice with a codimension-two right angle corner, topological invariants related to corner states are provided through extensions of bulk Hamiltonians.
