Quantum walks and orbital states of a Weyl particle

Journal Article · Fri Jul 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.012316· OSTI ID:20718324

Katori, Makoto; Fujino, Soichi ^[1]; Konno, Norio ^[2]

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1. Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551 (Japan)
2. Department of Applied Mathematics, Yokohama National University, 79-5 Tokiwadai, Yokohama 240-8501 (Japan)

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 [-{pi},{pi}). 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.

• OSTI ID: 20718324
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
DISTRIBUTION FUNCTIONS
EIGENSTATES
INFORMATION THEORY
ONE-DIMENSIONAL CALCULATIONS
ORBITS
QUANTUM MECHANICS
RANDOMNESS
SPACE
SPIN
THREE-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS