# Order, Chaos and (Quasi-) Dynamical Symmetries across 1st-order Quantum Phase Transitions in Nuclei

## TL;DR

This paper investigates the coexistence of regular and chaotic dynamics across first-order quantum phase transitions in nuclei, revealing distinct behaviors in spherical and deformed phases using the IBM Hamiltonian.

## Contribution

It demonstrates the contrasting regularity and chaos in nuclear phases and identifies quasi-SU(3) rotational bands in the deformed phase at high energies.

## Key findings

- Deformed phase exhibits complete regularity.
- Spherical phase shows highly chaotic dynamics.
- Quasi-SU(3) rotational bands are observed at high excitation energies.

## Abstract

First order quantum phase transition (QPT) between spherical and axially deformed nuclei shows coexisting, but well-separated regions of regular and chaotic dynamics. We employ a Hamiltonian of the Arima-Iachello Interacting Boson Model (IBM) with an arbitrarily high potential barrier separating the phases. Classical and quantum analyses reveal markedly distinct behavior of the two phases: Deformed phase is completely regular, while the spherical phase shows highly chaotic dynamics, similar to the H\'enon-Heiles system. Rotational bands with quasi-SU(3) characteristics built upon the regular vibrational spectrum of beta- and gamma-vibrations are observed in the deformed phase up to very high excitation energies.