Presentation Information
[18p-WL2_201-10]An integral representation of the wave function of a quantum walk on the regular tree
〇Seiken Saito1 (1.Kogakuin Univ.)
Keywords:
doressed photon,quantum walks,graph
In this study, we address continuous-time one-state quantum walks on the regular tree. Specifically, we examine a model where the time evolution matrix is given by the exponential of the adjacency matrix of the regular tree. We examine the wave function obtained using a concrete representation based on geometric quantities of the time evolution matrix as an extension of Bessel functions. Furthermore, we provide an integral representation corresponding to Bessel functions in this case. We also investigate properties of the wave function related to this integral representation.