We investigate the origin of spectral collapse occurring in nonlinear Rabi Hamiltonians with an su(1,1) coupling scheme, showing how the collapse can be triggered by the competition between the Rabi parameter g and the field frequency W. The collapse already appears in the model Hamiltonian where the atomic-energy term is absent. After showing that su(1,1) is the dynamical algebra of the Hamiltonian, we demonstrate how the occurrence of spectral collapse can be directly related to the three types of equivalence classes characterizing the structure of this algebra. We highlight how the dramatic change of the spectrum significantly affects the structure of eigenstates represented in a suitable momentum–coordinate picture.

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The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.

We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic¯eld and the two-level atom depends on the¯eld intensity. Upon modeling the matter-radiation coupling through the Holstein-Primako® realization of algebra suð1; 1Þ, we evaluate¯rst-and second-order eigenenergies and eigenstates both in the weakcoupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the¯rst case, among various e®ects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the suð1; 1Þ-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.

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