Arnold's potentials and quantum catastrophes II

Miloslav Znojil; Denis I. Borisov

doi:10.1016/j.aop.2022.168896

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arXiv · 2101.02015

Arnold's potentials and quantum catastrophes II

Miloslav Znojil·Denis I. Borisov

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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 $N-$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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Miloslav Znojil, Denis I. Borisov. 2022-04-29. Arnold's potentials and quantum catastrophes II. https://doi.org/10.1016/j.aop.2022.168896

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