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Approximation des phases aléatoires self-consistante dans l'étude de la superfluidité des systèmes fermioniques

Abstract : The Self-consistent random phase approximation (SCRPA) is a method which allows to include in the mean field theory the correlations in the groundstate and the excited states. It then constitutes a method of the mean field type for quantum fluctuations. It has the advantage to respect the Pauli principle, contrary to the standard RPA which is based on an approximation known as quasi-bosons. Furthermore, the SCRPA can be formulated from a variationnal principle.
We present the SCRPA method for the description of superfluid Fermi systems by using its Quasi-parhicle version (SCQRPA). A detailed study of the transition from normal to superfluid phase as well as a discussion of the soft mode which generates breaking of the particle number symmetry are presented. As an application, we treat the two-level pairing model which is an exactly soluble model. Good results are obtained in comparison with the exact ones. The nature of the spurious mode in SCQRPA is identified. A strong reduction of the number fluctuation in the SCQRPA vs BCS method is established. The transition from superfluidity to the normal fluid phase is carefully studied. A new method for the calculation of the occupation numbers is presented.
The success of the SCQRPA method is also present in the case of a model which mixes fermions and bosons such as the Da-Providencia-Schütte model. There is however a problem concerning the spurious mode which should be still investigated.
In the case of the seniority model, one shows than the SCQRPA method allows in a natural way to restore a particle number symmetry spontaneously broken at the mean field level. This is achieved via the introduction of a second Lagrange parameter which constrains the variance of the symmetry operator to zero. This important feature of the SCQRPA method, is pointed out for the first time.
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Submitted on : Friday, September 5, 2003 - 10:17:58 AM
Last modification on : Tuesday, November 19, 2019 - 2:39:38 AM
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  • HAL Id : tel-00003303, version 1



Aziz. Rabhi. Approximation des phases aléatoires self-consistante dans l'étude de la superfluidité des systèmes fermioniques. Physique mathématique [math-ph]. Université Claude Bernard - Lyon I, 2002. Français. ⟨tel-00003303⟩



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