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We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f= n? 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f2 even or odd), the models have both first- and second-order phase transitions only if f= 5, 9, 13, .. In the other f2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials. [ABSTRACT FROM AUTHOR]

We study the focus–focus type of monodromy in an integrable version of the Dicke model. Classical orbits forming a pinched torus represent analogues of the dynamic superradiance under conditions of a closed system. Quantum signatures of monodromy appear in lattices of expectation values of various quantities in the Hamiltonian eigenstates and are related to an excited-state quantum phase transition. We demonstrate the breakdown of these structures with an increasing strength of non-integrable perturbation. [ABSTRACT FROM AUTHOR]

A non-Euclidean geometric criterion for chaos (Horwitz et al 2007 Phys. Rev. Lett.98 234301) is investigated in bound systems with two degrees of freedom. It is shown that the criterion is partly equivalent to a simpler indicator of chaos based on the shape of equipotential curves. The method is numerically tested in a restricted Bohr model and in an extended Creagh–Whelan model. Although in some cases the geometric criterion approximately predicts the onset of chaos at low energies, manifest counterexamples disproving its general applicability are demonstrated. [ABSTRACT FROM AUTHOR]