Quantum walks and orbital states of a Weyl particle (9 pages)
Quantum walks and orbital states of a Weyl particle (9 pages)
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外尔粒子的量子行走和轨道态（9 页）
DOI：
10.1103/physreva.72.012316
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
N. Konno
中科院分区：
文献类型：
--
作者：
M. Katori;Soichi Fujino;N. Konno
一维量子步行者的时间演化方程精确地映射到自旋为1/2的零质量粒子的三维Weyl方程，其中步行者的波函数的每个波数k映射到三维动量空间中的点q（k），并且q（k）随着k在[-{pi}，{pi}）中的值的变化而形成平面轨道。为量子步行者提供实空间波函数的k上的积分对应于考虑外尔粒子的轨道状态，其被定义为自由外尔方程的能量-动量本征态沿轨道的沿着叠加（曲线积分）。Konno的量子步行者在长时间极限下的赝速度的新分布函数完全由轨道的形状以及轨道如何嵌入三维动量空间来控制。轨道态族可以看作是酉群U（2）的几何表示，本研究将为量子行走问题提出一个新的群论观点.
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.