Dirac quantum walks with conserved angular momentum

TL;DR

This paper constructs a quantum walk simulating the 2D Dirac equation on a polar grid, incorporating electromagnetic coupling and explicitly computing relativistic Landau levels.

Contribution

It introduces a novel quantum walk model for the Dirac equation on a polar grid, including electromagnetic interactions and Landau level simulations.

Findings

Quantum walk simulates 2D Dirac equation on polar grid

Coupling with electromagnetic fields demonstrated

Relativistic Landau levels explicitly computed and simulated

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.