TY  - JOUR
AU  - Hinarejos, M.
AU  - Perez, A.
AU  - Roldan, E.
AU  - Romanelli, A.
AU  - de Valcarcel, G. J.
PY  - 2013
DA  - 2013//
TI  - Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more
T2  - New J. Phys.
JO  - New Journal of Physics
SP  - 073041
EP  - 31pp
VL  - 15
PB  - Iop Publishing Ltd
AB  - The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented.
SN  - 1367-2630
UR  - http://arxiv.org/abs/1212.3600
UR  - https://doi.org/10.1088/1367-2630/15/7/073041
DO  - 10.1088/1367-2630/15/7/073041
LA  - English
N1  - WOS:000322110600003
ID  - Hinarejos_etal2013
ER  -