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Progress of Theoretical Physics

On the Random Phase Approximation Based on the Thermo Field Dynamics Formalism

M. Yamamura, João da Providência, A. Kuriyama, Carlos Fiolhais

Published Apr 1, 1990• 7 citations
Publisher

Abstract

A comparative study of the random phase approximation is reported in the case of the following three approaches based on the thermo field dynamics formalism: (A) the Tanabe approach, (B) the Hatsuda approach and (C) the approach developed by the present authors. The basic viewpoint is to formulate the random phase approximation by picking up the quadratic terms with respect to bosons in the boson expansion theory for the thermo field dynamics formalism. It is concluded that the approach (C) appears to be superior to the other two approaches.

DOI
10.1143/ptp.83.749

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A comparative study of the random phase approximation is reported in the case of the following three approaches based on the thermo field dynamics formalism: (A) the Tanabe approach, (B) the Hatsuda approach and (C) the approach developed by the present authors. The basic viewpoint is to formulate the random phase approximation by picking up the quadratic terms with respect to bosons in the boson expansion theory for the thermo field dynamics formalism. It is concluded that the approach (C) appears to be superior to the other two approaches.
A new boson expansion theory based on the random phase approximation is presented. The boson expansions are derived here directly in the random phase approximation representation with the help of a technique that combines the use of the Usui operator with that of a new bosonization procedure, called the term-by-term bosonization method. The present boson expansion theory is constructed by retaining a single collective quadrupole random phase approximation component, a truncation that allows for a perturbative treatment of the whole problem. Both Hermitian, as well as non-Hermitian boson expansions, valid for even nuclei, are obtained.
To take systematic account of thermal correlation effect on the mean field, the thermal random phase approximation formalism is extended based on the thermofield dynamics scheme. The random phase approximation phonon operator is expressed in terms of the thermofield dynamics quasiparticle operators with a tilde as well as those without a tilde, and the increase of the dimensionality of variational parameter manifold enables us to derive the extended thermal random phase approximation equation from deeper minimum of grand potential. It is shown that the extended thermal random phase approximation equation is justified also from viewpoint of time-dependent formalism. The method of constrained variation applied to the first extended thermal random phase approximation can be straightforwardly generalized to the second, or higher extended thermal random phase approximation. Extended expressions are given also for the stability condition of thermal Hartree-Fock-Bogoliubov approximation and the energy-weighted sum rule.
The usefulness of the quon expansion to treat Pauli principle violations and many-body correlations in many-fermion systems is investigated within two models, namely, the Lipkin and the two level pairing models. The q deformation parameter of the quon algebra is fixed through a dynamical criterion. The spectra obtained are compared with the random-phase approximation (RPA), usual boson expansion, and exact results. The quonic expansion is shown to take into account correlations which are not included either in the second order boson expansion or in the RPA approach.