标题： 一种对一维严格局部算子的拓扑不变量的构造性方法 显示英文标题

标题： A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators

摘要： 在本文中，我们将关注一维严格局部算子，这一概念在离散时间量子行走的一维整数格点背景下自然出现。 特别是，我们给出一种基本的构造性方法，来处理与这些算子相关的两个拓扑不变量：Fredholm指标和本质谱。 作为直接应用，我们将显式计算并完全分类一个著名的量子行走模型的这些拓扑不变量。 显示英文摘要

摘要： In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary constructive approach to the following two topological invariants associated with such operators: Fredholm index and essential spectrum. As a direct application, we shall explicitly compute and fully classify these topological invariants for a well-known quantum walk model.