论文标题
背景磁场中中性自旋1/2粒子的阿贝尔和非阿布尔拓扑行为
Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field
论文作者
论文摘要
我们介绍了一个数值实验的结果，其中经受静态磁涡流场的中性自旋1/2粒子通过双缝隙屏障。我们证明，检测屏幕上所得的干扰模式表现出使人联想到磁通管散射Aharonov-bohm的条纹。为了更好地了解观察到的行为，我们为上述磁场中的中性自旋1/2刚性平面转子提供了分析溶液。我们演示了该系统如何由于有效的Wu-Yang（WY）通量管出现而表现出非亚伯式Aharonov-Bohm效应。我们研究仪表不变分区函数的行为，并证明了自旋1/2平面转子的拓扑相变。我们为分区函数提供了一种表达式，其中它对WY量规势的Wilson Loop积分的依赖性是明确的。我们将其推广到Spin-1系统，以便在完整的量子设置中探索Wilzcek-Zee（WZ）机制。我们展示了如何通过改变半古典，非亚伯利亚，WZ相的高阶校正来解除堕落。允许分析描述的模型为反对意见提供了一种质疑基于原子和分子系统中广义的Born-oppenheimer近似的预测性的反对意见。 尽管这项研究的主要重点涉及中性系统中规结构的出现，但该理论也适用于具有电荷的系统。在这种情况下，我们探讨了具有有效量规电位的基本规范场（即电磁）之间的干扰。我们在离子陷阱设置中提出了后者可能的实验室演示。我们说明有效规范电位如何影响上述离子陷阱中的波动包装。
We present results of a numerical experiment in which a neutral spin-1/2 particle subjected to a static magnetic vortex field passes through a double-slit barrier. We demonstrate that the resulting interference pattern on a detection screen exhibits fringes reminiscent of Aharonov-Bohm scattering by a magnetic flux tube. To gain better understanding of the observed behavior, we provide analytic solutions for a neutral spin-1/2 rigid planar rotor in the aforementioned magnetic field. We demonstrate how that system exhibits a non-Abelian Aharonov-Bohm effect due to the emergence of an effective Wu-Yang (WY)flux tube. We study the behavior of the gauge invariant partition function and demonstrate a topological phase transition for the spin-1/2 planar rotor. We provide an expression for the partition function in which its dependence on the Wilson loop integral of the WY gauge potential is explicit. We generalize to a spin-1 system in order to explore the Wilzcek-Zee (WZ) mechanism in a full quantum setting. We show how degeneracy can be lifted by higher order gauge corrections that alter the semi-classical, non-Abelian, WZ phase. Models that allow analytic description offer a foil to objections that question the fidelity of predictions based on the generalized Born-Oppenheimer approximation in atomic and molecular systems. Though the primary focus of this study concerns the emergence of gauge structure in neutral systems, the theory is also applicable to systems that posses electric charge. In that case, we explore interference between fundamental gauge fields (i.e. electromagnetism) with effective gauge potentials. We propose a possible laboratory demonstration for the latter in an ion trap setting. We illustrate how effective gauge potentials influence wave-packet revivals in the said ion trap.
