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

• URL: http://arxiv.org/abs/2304.06464v2
• Date: Sun, 3 Sep 2023 14:11:41 GMT
• Title: Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian
• Authors: Takuya Machida
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 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.

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