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

TL;DR

This paper applies catastrophe theory to analyze quantum phase transitions in a nuclear cluster model with deformation and an effective QCD model, revealing insights into phase changes in complex many-body systems.

Contribution

It extends previous work by including deformed clusters and demonstrates the universal applicability of catastrophe theory to nuclear and QCD phase transitions.

Findings

Signatures of quantum phase transitions in deformed clusters.

Catastrophe theory provides insights into the perturbative to non-perturbative vacuum transition.

Numerical spectrum analysis confirms phase transition signatures.

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.