TY  - JOUR
AU  - Marquez-Martin, I.
AU  - Arnault, P.
AU  - Di Molfetta, G.
AU  - Perez, A.
PY  - 2018
DA  - 2018//
TI  - Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
T2  - Phys. Rev. A
JO  - Physical Review A
SP  - 032333
EP  - 8pp
VL  - 98
IS  - 3
PB  - Amer Physical Soc
AB  - Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation and the conserved current satisfies the corresponding conservation equation.
SN  - 2469-9926
UR  - http://arxiv.org/abs/1808.04488
UR  - https://doi.org/10.1103/PhysRevA.98.032333
DO  - 10.1103/PhysRevA.98.032333
LA  - English
N1  - WOS:000446163200006
ID  - Marquez-Martin_etal2018
ER  -