Quantum walks and orbital states of a Weyl particle

Details Quantum walks and orbital states of a Weyl particle Quantum walks and orbital states of a Weyl particle

2005-03-16

arxiv.org/abs/quant-ph/0503142v2

Phys.Rev. A72 (2005) 012316

Physics

Quantum Physics

REVTeX4, 9 pages, 1 figure, v2: Minor corrections made for publication in Phys.Rev.A

Scientific paper

10.1103/PhysRevA.72.012316

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 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 [-\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 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.

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