Interplay of order and chaos across a first-order quantum shape-phase transition in nuclei

We study the nature of the dynamics in a first-order quantum phase transition between spherical and prolate-deformed nuclear shapes. Classical and quantum analyses reveal a change in the system from a chaotic H\'enon-Heiles behavior on the spherical side into a pronounced regular dynamics on the deformed side. Both order and chaos persist in the coexistence region and their interplay reflects the Landau potential landscape and the impact of collective rotations.