A new method to building Dirac quantum walks coupled to electromagnetic fields
Abstract
A quantum walk whose continuous limit coincides with Dirac equation is usually called a Dirac Quantum Walk (DQW). A new systematic method to build DQWs coupled to electromagnetic (EM) fields is introduced and put to test on several examples of increasing difficulty. It is first used to derive the EM coupling of a well-known walk on the cubic lattice. Recently introduced DQWs on the triangular and honeycomb lattice are then re-derived, showing for the first time that these are the only DQWs that can be defined with spinors living on the vertices of these lattices. As a third example of the method's effectiveness, a new walk on a parallelepiped lattice is derived. As a fourth, negative example, it is shown that certain lattices like the rhombohedral lattice cannot be used to build DQWs. The effect of changing representation in the Dirac equation is also discussed.
Cite
@article{arxiv.1812.06729,
title = {A new method to building Dirac quantum walks coupled to electromagnetic fields},
author = {Gareth Jay and Fabrice Debbasch and J. B. Wang},
journal= {arXiv preprint arXiv:1812.06729},
year = {2018}
}