Confluences of exceptional points and a systematic classification of quantum catastrophes

DOI10.1038/S41598-022-07345-7arXiv2202.02554MaRDI QIDQ6390221

Publication date: 5 February 2022

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 o g^{(E P)}

.

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