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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

AutorHinarejos Doménech, Margarida ; Pérez Cañellas, Armando ; Roldán, Eugenio; Romanelli, Alejandro; Valcárcel Gonzalvo, Germán J. de
Palabras claveGraphene
Fecha de publicación23-jul-2013
EditorInstitute of Physics Publishing
CitaciónNew Journal of Physics 15: 073041 - 31 (2013)
ResumenThe 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.
Versión del editorhttp://dx.doi.org/10.1088/1367-2630/15/7/073041
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