Eigenvalues of quantum walk induced by recurrence properties of the underlying birth and death process: application to computation of an edge state

Abstract

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.

Research on M/M/1 Queue of Exponential Departure Intensity

“…Statistical balance theory of birth and death process is given in reference [4]. On the basis of balance theory, we can reach the conclusion that in ow of each state should be equal to out ow in a steady condition.…”