论文标题
量子和相关随机步行的返回概率
Return probability of quantum and correlated random walks
论文作者
论文摘要
对回报概率的分析是对经典随机步行研究的最重要和基本主题之一。在本文中，我们研究了通过路径计数方法在一维整个晶格中量子的回报概率和相关的随机步行。我们表明，量子和相关随机步行的回报概率可以用legendre多项式表示。此外，返回概率的生成函数可以用量子步行的第一和第二种椭圆形积分来编写。
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk.
