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 (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.