Multi-dimensional continuous time quantum walks related to the birth and death chains

TL;DR

This paper explores multi-dimensional continuous time quantum walks linked to birth and death chains, revealing independence properties and Gaussian convergence, with applications to path graphs and the Ehrenfest model.

Contribution

It introduces a new analysis of CTQW related to multi-dimensional birth and death chains, highlighting independence and convergence properties.

Findings

Time scaled independence between dimensions in CTQW

Convergence to Gaussian distribution for related random variables

Application to path graphs and Ehrenfest model

Abstract

In this paper, we consider multi-dimensional birth and death chains and continuous time quantum walks (CTQW) related to them. For CTQW related to our forms of multi-dimensional birth and death chains, we obtain the time scaled independence between multiple dimensions about the transition probability of CTQW. By using this feature, we analyze CTQW on the path graph, which is related to 1-dimensional Ehrenfest model. We also have a random variable which is related to our models and converges to the standard Gaussian distribution.