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Annals of Physics

The Gaussian Approximation About an Arbitrary Finite Temperature Mean-Field

G. Puddu

Published Sep 1, 1994• 0 citations
Publisher
DOI
10.1006/aphy.1994.1087

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Analogies and differences between the random phase approximation (RPA) and the Gaussian approximation at finite temperature are discussed. A comparison is made for Hartree and Hartree-Fock temperature dependent mean fields. Some ambiguities, in the definition of the Hartree mean field and in the relative correction, are analyzed. In a solvable model with a repulsive potential, the Gaussian approximation and the RPA, both built from the Hartree mean field, are found more reliable than the RPA built from a Hartree-Fock mean field.
Properties of Bose–Einstein condensates (BEC) are studied in the presence of a Gaussian random potential of arbitrary strength of disorder and with arbitrary correlation length. Using the stochastic mean field approximation, a system having arbitrary strength of interactions is treated at finite temperature. A special case, in which we assume that the second moment of the random potential is Lorentzian, is treated in more detail at zero temperature. The total density of particles consists of condensate density, glassy density and normal density components. Our results are in agreement with those of Huang and Meng (HM). The system is stable below the critical value of the disorder parameter and undergoes a first-order phase transition at the critical value. We find that the critical value of the disorder parameter changes with changing the correlation length of the random potential.
We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of mean-field type equations and whose results at the lowest level are identically the same as those of the Gaussian effective potential approach and the mean-field approach. The great advantageous point of this formulation is its readiness of applicability to time-dependent quantum systems and to finite temperature field theory, and its possibility to go beyond the Gaussian approximation.