Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X(5), -X(5), and E(5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the (η, χ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed. The text was submitted by the authors in English.