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Journal of Physics A Mathematical and General

Pairing interaction and its q-deformed versions

Sidney S. Avancini, Débora Peres Menezes

Published Nov 21, 1993• 7 citations
Publisher

Abstract

We investigate the behaviour of the pairing model within the context of quantum algebras. The pairing Hamiltonian is diagonalized exactly for different values of the deformation parameter q in systems with 8 and 50 particles. The same Hamiltonian is solved with the help of the coherent state variational method. We find that the variational method gives reliable results when compared with the exact ones. We also discuss the differences between the two deformation procedures.

DOI
10.1088/0305-4470/26/22/025

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We investigate the behaviour of the pairing model within the context of quantum algebras. The pairing Hamiltonian is diagonalized exactly for different values of the deformation parameter q in systems with 8 and 50 particles. The same Hamiltonian is solved with the help of the coherent state variational method. We find that the variational method gives reliable results when compared with the exact ones. We also discuss the differences between the two deformation procedures.
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.
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)_q- and the su(1,1)_q-algebras are obtained in the form expressed in terms of four kinds of boson operators. As an illustrative example of the application, the framework for describing thermal effects observed in two-level shell model under the pairing correlation is proposed.
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)_q- and the su(1,1)_q-algebras are obtained in the form expressed in terms of four kinds of boson operators. As an illustrative example of the application, the framework for describing thermal effects observed in two-level shell model under the pairing correlation is proposed.
The basic idea presented in Parts (I) – (III) of this series for the deformed boson scheme is applied to the case of the su(2)- and the su(1, 1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)q- and the su(1, 1)q-algebras are obtained in forms expressed in terms of four kinds of boson operators. As an illustrative example demonstrating the application of the deformed boson scheme, the framework for describing thermal effects observed in the two-level shell model with pairing correlation is proposed.