Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk
Quantum Physics
2021-12-17 v2
Abstract
In this paper, we consider the stationary measure of the Hadamard walk on the one-dimensional integer lattice. Here all the stationary measures given by solving the eigenvalue problem are completely determined via the transfer matrix method. Then these stationary measures can be divided into three classes, i.e., quadratic polynomial, bounded, and exponential types. In particular, we present an explicit necessary and sufficient condition for the bounded-type stationary measure to be periodic.
Cite
@article{arxiv.1905.00330,
title = {Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk},
author = {Takashi Komatsu and Norio Konno},
journal= {arXiv preprint arXiv:1905.00330},
year = {2021}
}
Comments
28 pages, Journal of Statistical Physics (in press)