In this paper, we consider an extended coined Szegedy model and discuss the existence of the point spectrum of induced quantum walks in terms of recurrence properties of the underlying birth and death process. We obtain that if the underlying random walk is not null recurrent, then the point spectrum exists in the induced quantum walks. As an application, we provide a simple computational way of the dispersion relation of the edge state part for the topological phase model driven by quantum walk using the recurrence properties of underlying birth and death process.

中文翻译：

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由潜在的生与死过程的递归特性引起的量子游动的特征值：在边缘状态计算中的应用

在本文中，我们考虑了扩展的Szegedy模型，并根据潜在的生与死过程的递归性质讨论了诱导的量子游走的点谱的存在。我们获得的结果是，如果潜在的随机游走不是零循环的，那么点频谱就存在于诱导的量子游走中。作为一种应用，我们使用基本生死过程的递归性质，为量子游走驱动的拓扑相位模型提供了一种简单的边缘状态部分色散关系计算方法。