Limit distributions of two-dimensional quantum walks

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dc.creatorWatabe, Kyohei
dc.creatorKobayashi, Naoki
dc.creatorKatori, Makoto
dc.creatorKonno, Norio
dc.date2008-02-20
dc.date2008-06-20
dc.date.accessioned2026-07-07T09:45:30Z
dc.date.available2026-07-07T09:45:30Z
dc.descriptionOne-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two components of walker's pseudovelocity, $X_t/t$ and $Y_t/t$, is proved and the probability density of limit distribution is derived. Dependence of the two-dimensional limit density function on the parameter of quantum coin and initial four-component qudit of quantum walker is determined. Symmetry of limit distribution on a plane and localization around the origin are completely controlled. Comparison with numerical results of direct computer-simulations is also shown.
dc.descriptionv3: REVTeX4, 20 pages, 6 figures, minor corrections made for publication
dc.identifierhttps://arxiv.org/abs/0802.2749
dc.identifierhttp://arxiv.org/abs/0802.2749
dc.identifierPhys. Rev. A77 (2008) 062331/1-9
dc.identifierdoi:10.1103/PhysRevA.77.062331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163214
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleLimit distributions of two-dimensional quantum walks
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