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Journal of Physics A Mathematical and General

Dynamics of the q-deformed Lipkin model

Sidney S. Avancini, Débora Peres Menezes, Mello Moraes, F. Cruz

Published Feb 7, 1994• 8 citations
Publisher

Abstract

In this paper we investigate the dynamics of the Lipkin-Meshkov-Glick model within the context of quantum algebras. For this purpose we obtain the equations of motion with the help of the time-dependent variational principle. To analyse the results, graphs for equi-energies, potentials and mean-square deviation of the J z operator have been plotted. Modifications in the usual libration and rotational motions due to the introduction of quantum deformation are discussed.

DOI
10.1088/0305-4470/27/3/024

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Assuming q-deformed commutation relations for the fermions, an extension of the standard Lipkin Hamiltonian is presented. The usual quasi-spin representation of the standard Lipkin model is also obtained in this q-deformed framework. A variationally obtained energy functional is used to analyse the phase transition associated with the spherical symmetry breaking. The only phase transitions in this q-deformed model are of second order. As an outcome of this analysis a critical parameter is obtained which is dependent on the deformation of the algebra and on the number of particles.