Quantum walks and orbital states of a Weyl particle

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dc.creatorKatori, Makoto
dc.creatorFujino, Soichi
dc.creatorKonno, Norio
dc.date2005-03-16
dc.date2005-05-18
dc.date.accessioned2026-07-07T06:12:24Z
dc.date.available2026-07-07T06:12:24Z
dc.descriptionThe time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point \vec{q}(k) in the three-dimensional momentum space and \vec{q}(k) makes a planar orbit as k changes its value in [-π, π). The integration over k providing the real-space wave function for a quantum walker corresponds to considering an orbital state of a Weyl particle, which is defined as a superposition (curvilinear integration) of the energy-momentum eigenstates of a free Weyl equation along the orbit. Konno's novel distribution function of quantum-walker's pseudo-velocities in the long-time limit is fully controlled by the shape of the orbit and how the orbit is embedded in the three-dimensional momentum space. The family of orbital states can be regarded as a geometrical representation of the unitary group U(2) and the present study will propose a new group-theoretical point of view for quantum-walk problems.
dc.descriptionREVTeX4, 9 pages, 1 figure, v2: Minor corrections made for publication in Phys.Rev.A
dc.identifierhttps://arxiv.org/abs/quant-ph/0503142
dc.identifierhttp://arxiv.org/abs/quant-ph/0503142
dc.identifierPhys.Rev. A72 (2005) 012316
dc.identifierdoi:10.1103/PhysRevA.72.012316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92774
dc.subjectQuantum Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleQuantum walks and orbital states of a Weyl particle
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