dorsal/arxiv
View SchemaQuantum walks and orbital states of a Weyl particle
| Authors | Makoto Katori, Soichi Fujino, Norio Konno |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503142 |
| URL | https://arxiv.org/abs/quant-ph/0503142 |
| DOI | 10.1103/PhysRevA.72.012316 |
| Journal | Phys.Rev. A72 (2005) 012316 |
Abstract
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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"abstract": "The time-evolution equation of a one-dimensional quantum walker is exactly\nmapped to the three-dimensional Weyl equation for a zero-mass particle with\nspin 1/2, in which each wave number k of walker\u0027s wave function is mapped to a\npoint \\vec{q}(k) in the three-dimensional momentum space and \\vec{q}(k) makes a\nplanar orbit as k changes its value in [-\\pi, \\pi). The integration over k\nproviding the real-space wave function for a quantum walker corresponds to\nconsidering an orbital state of a Weyl particle, which is defined as a\nsuperposition (curvilinear integration) of the energy-momentum eigenstates of a\nfree Weyl equation along the orbit. Konno\u0027s novel distribution function of\nquantum-walker\u0027s pseudo-velocities in the long-time limit is fully controlled\nby the shape of the orbit and how the orbit is embedded in the\nthree-dimensional momentum space. The family of orbital states can be regarded\nas a geometrical representation of the unitary group U(2) and the present study\nwill propose a new group-theoretical point of view for quantum-walk problems.",
"arxiv_id": "quant-ph/0503142",
"authors": [
"Makoto Katori",
"Soichi Fujino",
"Norio Konno"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1103/PhysRevA.72.012316",
"journal_ref": "Phys.Rev. A72 (2005) 012316",
"title": "Quantum walks and orbital states of a Weyl particle",
"url": "https://arxiv.org/abs/quant-ph/0503142"
},
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