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arXiv · 2007.06211

Dirac quantum walks with conserved angular momentum

Gareth Jay·Pablo Arnault·Fabrice Debbasch
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Abstract

A Quantum Walk (QW) simulating the flat $(1 + 2)$D Dirac Eq.\ on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group, but rather of its double cover, the QW can only be defined globally on an extended spacetime where the polar angle extends from $0$ to $4 \pi$. The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac Eq.\ are computed explicitly and simulated by the QW.

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Gareth Jay, Pablo Arnault, Fabrice Debbasch. 2020-07-13. Dirac quantum walks with conserved angular momentum. https://arxiv.org/abs/2007.06211

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