Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more
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Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more

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Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more

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Hinarejos Doménech, Margarida; Pérez Cañellas, Armando; Roldán Serrano, Eugenio; Romanelli, A.; Valcárcel Gonzalvo, Germán J. de
This document is a artículoDate2013

Este documento está disponible también en : http://hdl.handle.net/10550/42962
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.

    Hinarejos Doménech, Margarida Pérez Cañellas, Armando Roldán Serrano, Eugenio Romanelli, A. Valcárcel Gonzalvo, Germán José de 2013 Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more New Journal of Physics 15 073041-1 073041-31
http://dx.doi.org/10.1088/1367-2630/15/7/073041

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