Dirac quantum walks with conserved angular momentum
Quantum Physics
2020-07-21 v2
Abstract
A Quantum Walk (QW) simulating the flat 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 to . 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.
Cite
@article{arxiv.2007.06211,
title = {Dirac quantum walks with conserved angular momentum},
author = {Gareth Jay and Pablo Arnault and Fabrice Debbasch},
journal= {arXiv preprint arXiv:2007.06211},
year = {2020}
}