Confluences of exceptional points and a systematic classification of quantum catastrophes

• URL: http://arxiv.org/abs/2202.02554v1
• Date: Sat, 5 Feb 2022 13:41:08 GMT
• Title: Confluences of exceptional points and a systematic classification of quantum catastrophes
• Authors: Miloslav Znojil
• Abstract summary: Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the corresponding parameter-dependent Hamiltonian $H(g)$) depends, naturally, on the formal mathematical characteristics of the EP. We illustrate and discuss, using several solvable toy models, some of the most elementary mechanisms of the EP-merger realization of the process of the transition $g to g(EP)$
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the corresponding parameter-dependent Hamiltonian $H(g)$) depends, naturally, on the formal mathematical characteristics of the EP, i.e., in essence, on its so called algebraic multiplicity $N$ and geometric multiplicity $K$. In our paper we assume that both of them are finite, and we illustrate and discuss, using several solvable toy models, some of the most elementary mechanisms of the EP-merger realization of the process of the transition $g \to g^{(EP)}$.

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