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

Abstract

Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\dots \right\}$, 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 asymmetric 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 symmetric density function.

15 pages, 5 figures

Cited by in corpus (1)

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