The Spectrum of Asymptotic Cayley Trees
Quantum Physics
2024-04-16 v2
Abstract
We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. We apply our results to studying continuous time quantum walk on these graphs. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.
Keywords
Cite
@article{arxiv.2312.09833,
title = {The Spectrum of Asymptotic Cayley Trees},
author = {Bergfinnur Durhuus and Thordur Jonsson and John Wheater},
journal= {arXiv preprint arXiv:2312.09833},
year = {2024}
}
Comments
21 pages, 1 figure. Revised version with extended Introduction, streamlined derivation of generating function relations, and with statement of Theorem 3 corrected