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Journal of Physics A Mathematical and General

Quantum algebraic description of the Moszkowski model

Débora Peres Menezes, Sidney S. Avancini, Constança Providência

Published Dec 7, 1992• 10 citations
Publisher

Abstract

The authors investigate the behaviour of the Moszkowski model (1958) within the context of quantum algebras. The Moszkowski Hamiltonian is diagonalized exactly for different numbers of particles and for various values of the deformation parameter of the quantum algebra involved. They also include cranking in the system and observe its variation as a function of the deformation parameters.

DOI
10.1088/0305-4470/25/23/026

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The authors investigate the behaviour of the Moszkowski model (1958) within the context of quantum algebras. The Moszkowski Hamiltonian is diagonalized exactly for different numbers of particles and for various values of the deformation parameter of the quantum algebra involved. They also include cranking in the system and observe its variation as a function of the deformation parameters.
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.
We investigate the consequences on the order/chaos transition of replacing the scalar rotational energy of the particles-rotor model by a one-body cranking term. The nearest-neighbor distribution of energy levels and the spectral rigidity are studied as a function of the spin or cranking frequency, respectively. Exact energies for our statistical analyses are obtained from a full diagonalization of a many-body Hamiltonian with two-body forces for six particles in an i13/2{\mathit{i}}_{13/2}i13/2​ shell coupled to a deformed core. In this model, the competing physical effects (two-body interaction strength, quadrupole deformation, and moment of inertia) are easily parametrized and studied. The dependence of the chaoticity on model parameters reveals the stabilizing influence of a large quadrupole deformation. For low spins, the considerable effects of the (effectively two-body) recoil term give significant differences between the two descriptions.