Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices

Chul Ki Ko, Norio Konno, Etsuo Segawa, Hyun Jae Yoo

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We consider the open quantum random walks on the crystal lattices and investigate the central limit theorems for the walks. On the integer lattices the open quantum random walks satisfy the central limit theorems as was shown by Attal et al (Ann Henri Poincaré 16(1):15–43, 2015). In this paper we prove the central limit theorems for the open quantum random walks on the crystal lattices. We then provide with some examples for the Hexagonal lattices. We also develop the Fourier analysis on the crystal lattices. This leads to construct the so called dual processes for the open quantum random walks. It amounts to get Fourier transform of the probability densities, and it is very useful when we compute the characteristic functions of the walks. In this paper we construct the dual processes for the open quantum random walks on the crystal lattices providing with some examples.

本文言語English
ページ(範囲)710-735
ページ数26
ジャーナルJournal of Statistical Physics
176
3
DOI
出版ステータスPublished - 2019 8月 15
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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