Arnold势与量子灾变II
Arnold's potentials and quantum catastrophes II
摘要：
众所周知的避免能级交叉（ALC）现象可以被看作是经典动力学系统中Thom灾变的量子模拟。一维薛定谔方程被用来说明。在建设性的方式，一个家庭的限制多项式的潜力被认为是，其特征在于存在一个$N-$的高障碍分离的$(N+1)-$小的深谷。在量子低激发谱中，自适应激光器显示了长时间经典平衡点的分岔。谷之间每一次隧道控制的微调主导切换最终都被解释为概率密度拓扑结构的变化，代表了真正的量子重定域灾难。
英文摘要：
The well known phenomenon of avoided level crossing (ALC) can be perceived as a quantum analogue of the Thom's catastrophes in classical dynamical systems. One-dimensional Schrödinger equation is chosen for illustration. In constructive manner, a family of confining polynomial potentials is considered, characterized by the presence of an $N-$plet of high barriers separating the $(N+1)-$plet of deep valleys. The bifurcations of the long-time classical equilibria are shown paralleled by the ALCs in the quantum low-lying spectra. Every tunneling-controlled fine-tuned switch of dominance between the valleys is finally interpreted as a change of the topological structure of the probability density representing a genuine quantum relocalization catastrophe.
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