Order, chaos and quasi-symmetries in a first-order quantum phase transition

Quantum phase transitions (QPTs) are structural changes in the properties of a physical system induced by a variation of parameters in the quantum Hamiltonian. In the present talk, we examine the order and chaos and persisting symmetries, accompanying a first-order QPT in nuclei. The Hamiltonian employed describes a QPT between spherical and deformed shapes, associated with U(5) and SU(3) dynamical symmetries, respectively. A classical analysis reveals a rich but simply-divided phase space structure with a Henon-Heiles type of chaotic dynamics ascribed to the spherical minimum, coexisting with a robustly regular dynamics ascribed to the deformed minimum in the Landau potential. A quantum analysis discloses regular U(5)-like multiplets in the spherical region and regular SU(3)-like rotational bands in the deformed region, which retain their identity amidst a complicated environment of other states. A symmetry analysis shows that these regular subsets of states, are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively.