论文标题
三孔和多孔电势中的Bions和Instantons
Bions and Instantons in Triple-well and Multi-well Potentials
论文作者
论文摘要
具有多个退化经典谐波最小值的量子系统表现出新的非扰动现象，这些现象对于双孔和周期性电势不存在。这个家族的最简单特征例子是三孔电位。尽管Instantons是具有有限和最小作用的确切的半经典溶液，但它们并没有为半经典分析中的领先顺序的能量谱系做出贡献。这是因为激体波动的预因剂消失了，可以将其解释为机械上的无限量子。相反，非扰动物理受不同类型的{\ it bion}配置的控制。还讨论了对超对称和准溶解模型的概括。拓扑结合和中性BION之间的一种有趣的干扰模式，具体取决于隐藏的拓扑角度，离散的theta角度和扰动水平的数量，导致了低谎言状态的分歧/收敛膨胀的复杂模式，并为某些州的精确溶解性提供了标准。我们使用Bender-Wu Mathematica软件包确认了这些半经典的预测，以研究相关的扰动扩展的结构。事实证明，我们研究的所有系统在三口井的扰动系数之间都有一个奇怪的确切一对一关系，我们使用Benderwu软件包检查了这三井。
Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the triple-well potential. Despite the fact that instantons are exact semiclassical solutions with finite and minimal action, they do not contribute to the energy spectrum at leading order in the semiclassical analysis. This is because the instanton fluctuation prefactor vanishes, which can be interpreted as the action becoming infinite quantum mechanically. Instead, the non-perturbative physics is governed by different types of {\it bion} configurations. A generalization to supersymmetric and quasi-exactly soluble models is also discussed. An interesting pattern of interference between topological and neutral bions, depending on the hidden topological angle, the discrete theta angle and the perturbative level number, leads to an intricate pattern of divergent/convergent expansions for low lying states, and provides criteria for the exact solvability of some of the states. We confirm these semiclassical bion predictions using the Bender-Wu Mathematica package to study the structure of the associated perturbative expansions. It also turns out that all the systems we study have a curious exact one-to-one relationship between the perturbative coefficients of the three wells, which we check using the BenderWu package.
