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Updated: Oct 1, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Confluences of exceptional points and a systematic classification of quantum catastrophes
Miloslav Znojil1,2,3
1The Czech Academy of Sciences, Nuclear Physics Institute, Hlavní 130, 250 68, Řež, Czech Republic. znojil@ujf.cas.cz.
Abstract:
In the problem of classification of the parameter-controlled quantum phase transitions, attention is turned from the conventional manipulations with the energy-level mergers at exceptional points to the control of mergers of the exceptional points themselves. What is obtained is an exhaustive classification which characterizes every phase transition by the algebraic and geometric multiplicity of the underlying confluent exceptional point. Typical qualitative characteristics of non-equivalent phase transitions are illustrated via a few elementary toy models.
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