An eigenfunction expansion formula for one-dimensional two-state quantum walks

Autor:	Tate, Tatsuya
Rok vydání:	2021
Předmět:	Mathematical Physics Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
DOI:	10.1007/s43034-022-00210-8
Popis:	The purpose of this paper is to give a direct proof of an eigenfunction expansion formula for one-dimensional 2-state quantum walks, which is an analog of that for Sturm-Liouville operators due to Weyl, Stone, Titchmarsh and Kodaira. In the context of the theory of CMV matrix it had been already established by Gesztesy-Zinchenko. Our approach is restricted to the class of quantum walks mentioned above whereas it is direct and it gives some important properties of Green functions. The properties given here enable us to give a concrete formula for a positive-matrix-valued measure, which gives directly the spectral measure, in a simplest case of the so-called two-phase model. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.09942 Zobrazit plný text záznamu View this record from Arxiv