2012/12/31 by Germán J. de Valcárcel, A. Pérez, Margarida Hinarejos +4 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Dispersion (optics) #Geometry #Mathematical physics #Mathematics #One-dimensional space #Perspective (graphical) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Random walk #Statistical physics #quant-ph
paper · pdf · doi:10.1088/1367-2630/15/7/073041
published in New Journal of Physics 15(7), 073041 (IOP Publishing) · 18 pages, 13 figures
arxiv created 2013/05/13 · openalex publication_date 2013/07/23 · arxiv updated 2014/01/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08
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 Schrödinger 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.