Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian

Takuya Machida

Published 2023-04-13Version 1

Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and its system is operated by a spatially periodic Hamiltonian. As a result, we see an asymmetry probability distribution. To catch a long-time behavior, we also try to find a long-time limit theorem and realize that the limit distribution holds a symmetry density function.