Related papers: Arnold's potentials and quantum catastrophes II

Arnold's potentials and quantum catastrophes II

URL: http://arxiv.org/abs/2101.02015v2
Date: Fri, 29 Apr 2022 08:07:03 GMT
Title: Arnold's potentials and quantum catastrophes II
Authors: Miloslav Znojil and Denis I. Borisov
Abstract summary: A family of confining 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 interpreted as a change of the topological structure of the probability density representing a genuine quantum relocalization catastrophe.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 Schr\"{o}dinger 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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