Germán J. de Valcárcel, Margarida Hinarejos, Eugenio Roldán, Armando Pérez, Alejandro Romanelli
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known behaviors 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 Schr\"odinger type, and allow devising interesting behaviors, such as the ballistic propagation without deformation or the generation of almost flat probability distributions, what is corroborated numerically. There are however special points where the energy surfaces display conical intersections (the so-called diabolical points) and, near them, the dynamics is entirely different, similar to that of massless particles or of electrons in graphene. Applications to the two-dimensional Grover walk are presented.
View original:
http://arxiv.org/abs/1212.3600
No comments:
Post a Comment