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Multi-Dimensional Quantum Walks: a Playground of Dirac and Schr\"{o}dinger Particles

Manami YamagishiNaomichi HatanoKen-Ichiro ImuraHideaki Obuse
Dec 2022
摘要
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whosecontinuum limit is the intrinsic multi-dimensional Dirac equation, which can befurther mapped to the Schr\"{o}dinger equation. We show in two ways that ourDTQW is an excellent measure to investigate the two-dimensional (2D) DiracHamiltonian. First, we show that the dynamics of our DTQW resembles that of a2D Schr\"{o}dinger harmonic oscillator. Second, we find in our DTQW topologicalfeatures of the Dirac system. By manipulating the coin operators, we cangenerate not only standard edge states but also corner states.
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