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Journal of Physics A Mathematical and General

The q-deformed Moszkowski model: RPA modes

Dennis Bonatsos A, Lucília P. Brito, Débora Peres Menezes, Constança Providência, João da Providência

Published Feb 21, 1993• 17 citations
Publisher

Abstract

The behaviour of the Moszkowski model within the context of quantum algebras is studied. The Moszkowski Hamiltonian is exactly diagonalized for various values of the deformation parameter of the involved quantum algebra. The phase transition from a vibrational regime to a rotational regime is discussed in terms of the q-deformation. A coherent state for the ground state is introduced, and the Hartree-Fock energy and the RPA frequencies are compared with the exact values. The meaning of the q-deformation in this model is discussed.

DOI
10.1088/0305-4470/26/4/016

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The behaviour of the Moszkowski model within the context of quantum algebras is studied. The Moszkowski Hamiltonian is exactly diagonalized for various values of the deformation parameter of the involved quantum algebra. The phase transition from a vibrational regime to a rotational regime is discussed in terms of the q-deformation. A coherent state for the ground state is introduced, and the Hartree-Fock energy and the RPA frequencies are compared with the exact values. The meaning of the q-deformation in this model is discussed.
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (qqq-numbers, qqq-analysis, qqq-oscillators, qqq-algebras), the suq_qq​(2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to molecular structure and an outlook are also given.
In this work we study the quantum deformation of the three-level Lipkin model. The exact spectra are obtained. The reliability of the mean-field approximation is discussed in the framework of the model. Using adequate coherent states, the mean-field ground-state and the random-phase-approximation modes are calculated. The Dyson realization of suq{\mathrm{su}}_{\mathit{q}}suq​(3) in the Bargmann representation is derived. The effect of the quantum deformation on the ground-state energy and on the phase transitions of the model is discussed. The simulation of temperature effects by the quantum deformation is investigated.
We suggest a model of q-deformed rotating oscillator which possesses the symmetry of quantum group and point out that this model can be used to describe the vibrational and rotational structures of many microscopic systems. We construct the representation of q-oscilla or algebra and give energy values of q-oscillaor in this representation. It is shown that the q-oscillator spectra can be used to describe infrared spectra, Raman spectra and vibrational structure of electronic transitions of diatomic molecules.