PT Journal
AU Jay, G
   Arnault, P
   Debbasch, F
TI Dirac quantum walks with conserved angular momentum
SO Quantum Studies-Mathematics and Foundations
JI Quantum Stud. Math. Found.
PY 2021
BP 419
EP 430
VL 8
DI 10.1007/s40509-021-00253-x
LA English
DE Quantum walks; Quantum simulation; Lattice field theory
AB A quantum walk (QW) simulating the flat (1+2)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO(3), but rather of its double cover SU(2), 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 equation are computed explicitly and simulated by the QW.
ER