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

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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)710-735
Number of pages26
JournalJournal of Statistical Physics
Volume176
Issue number3
DOIs
Publication statusPublished - 2019 Aug 15

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random walk
crystal lattices
Central limit theorem
Random walk
Crystal
theorems
Walk
Hexagonal Lattice
characteristic equations
Fourier Analysis
Fourier analysis
Characteristic Function
Probability Density
integers
Fourier transform
Integer

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Ko, Chul Ki ; Konno, Norio ; Segawa, Etsuo ; Yoo, Hyun Jae. / Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices. In: Journal of Statistical Physics. 2019 ; Vol. 176, No. 3. pp. 710-735.
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Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices. / Ko, Chul Ki; Konno, Norio; Segawa, Etsuo; Yoo, Hyun Jae.

In: Journal of Statistical Physics, Vol. 176, No. 3, 15.08.2019, p. 710-735.

Research output: Contribution to journalArticle

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