Phys. Rev. A 72, 012316 (2005) [9 pages]Quantum walks and orbital states of a Weyl particleSee Also: Publisher's Note Received 14 March 2005; published 14 July 2005; publisher error corrected 20 July 2005 The 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 the walker’s wave function is mapped to a point q(k) in the three-dimensional momentum space and 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 a quantum walker’s pseudovelocities 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. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.72.012316
DOI:
10.1103/PhysRevA.72.012316
PACS:
03.67.−a, 03.65.−w, 05.40.−a
See AlsoPublisher's Note: Makoto Katori, Soichi Fujino, and Norio Konno, Publisher's Note: Quantum walks and orbital states of a Weyl particle [Phys. Rev. A 72, 012316 (2005)], Phys. Rev. A 72, 019904 (2005). |
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