论文标题
用量子步行模拟非交换几何形状
Simulating Non Commutative Geometry with Quantum Walks
论文作者
论文摘要
在均匀的磁场中移动的带电粒子的背景下，考虑了非交换几何形状（NCG）。重新审视了经典和量子机械处理，并引入了NCG的新标记。然后，该标记用于研究磁量子步行中的NCG。事实证明，这些步道在连续限制的及其附近展示了NCG。对于纯粹的离散制度，全面研究了两个不同复杂性的说明性步行。最复杂的步行确实表现出NCG，但最简单，最简单的步行却没有。因此，NCG不仅可以在连续限制下，而且在纯离散方面都可以模拟NCG。
Non Commutative Geometry (NCG) is considered in the context of a charged particle moving in a uniform magnetic field. The classical and quantum mechanical treatments are revisited and a new marker of NCG is introduced. This marker is then used to investigate NCG in magnetic Quantum Walks. It is proven that these walks exhibit NCG at and near the continuum limit. For the purely discrete regime, two illustrative walks of different complexities are studied in full detail. The most complex walk does exhibit NCG but the simplest, most degenerate one does not. Thus, NCG can be simulated by QWs, not only in the continuum limit, but also in the purely discrete regime.
