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

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