Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD

Abstract

The catastrophe theory is applied to a nuclear cluster model and an effective model for QCD at low energy. The study of quantum phase transitions in the cluster model was considered in an earlier publication, but restricted to spherical clusters and on a semi-classical level. In the present contribution, we include the case of deformed clusters and determine the spectrum numerically as a function of an interaction parameter, where signatures of a quantum phase transition can be seen. It is shown that in this more complicated case, with deformation of the clusters, the catastrophe theory can be applied with some interesting consequences. A further example of a many-body problem is considered, namely an effective model of QCD, which is able to describe the low energy hadron spectrum and, when temperature is introduced, even ratios of particle-antiparticle productions. The catastrophe theory is able to provide useful information on the phase transition from a perturbative to a non-perturbative vacuum. This contributions shows the universal usefulness of catastrophe theory, while more examples of applications to different fields are mentioned in the Introduction.

25 pages, 10 figures

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• Excited state quantum phase transitions in many-body systems
• Symmetry-guided large-scale shell-model theory
• Algebraic models for shell-like quarteting of nucleons
• 16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle
• Quantum catastrophes from an algebraic perspective