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Pré-Publication, Document De Travail Année : 2015

Massless Dirac equation from Fibonacci discrete-time quantum walk

Lauchlan Honter
  • Fonction : Auteur
Ben Luo
  • Fonction : Auteur
Tatsuaki Wada
  • Fonction : Auteur
Yutaka Shikano
  • Fonction : Auteur

Résumé

Discrete-time quantum walks can be regarded as quantum dynamical simulators since they can simulate spatially discretized Schrödinger, massive Dirac, and Klein–Gordon equations. Here, two different types of Fibonacci discrete-time quantum walks are studied analytically. The first is the Fibonacci coin sequence with a generalized Hadamard coin and demonstrates six-step periodic dynamics. The other model is assumed to have three- or six-step periodic dynamics with the Fibonacci sequence. We analytically show that these models have ballistic transportation properties and continuous limits identical to those of the massless Dirac equation with coin basis change.
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hal-03594752 , version 1 (14-03-2024)

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Di Molfetta Giuseppe, Lauchlan Honter, Ben Luo, Tatsuaki Wada, Yutaka Shikano. Massless Dirac equation from Fibonacci discrete-time quantum walk. 2024. ⟨hal-03594752⟩
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