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

In this paper, we consider multi-dimensional birth and death chains and continuous time quantum walks (CTQWs) related to them. For continuous time quantum walk (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.