Arnold's potentials and quantum catastrophes II
arXiv:2101.02015 · doi:10.1016/j.aop.2022.168896
Abstract
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 plet of high barriers separating the 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.
23 pp