Beyond Gross-Pitaevskii Mean-Field Theory

Martín Heimsoth, M. Bönitz

E. Brézin

Nick P. Proukakis

A large number of effects related to the phenomenon of Bose-Einstein Condensation (BEC) can be understood in terms of lowest order mean field theory, whereby the entire system is assumed to be condensed, with thermal and quantum fluctuations completely ignored [1]. Such a treatment leads to the Gross-Pitaevskii

Michael Schick C, Paul R. Zilsel

A formalism due to Langer which permits the derivation of the Gross-Pitaevskii (mean-field) theory of many-boson systems is applied to the ideal Bose gas, and the results obtained are compared with those of an exact treatment. With the exact solution known, it is shown that the order parameter is nonvanishing below the Bose condensation temperature. However, this information cannot be obtained from the mean-field theory alone, which indicates that no Gross-Pitaevskii equation can be derived for this system.

Dieter Vollhardt, Krzysztof Byczuk, Marcus Kollar

S. Stringari

Abstract Using the linearized version of the time dependent Gross–Pitaevskii equation, we calculate the dynamic response of a Bose–Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the fluctuation—dissipation theorem is used to evaluate the corresponding quantum fluctuations induced by the elementary excitations in the ground state. In uniform conditions the predictions of Bogoliubov theory, including the infrared divergency of the particle distribution function and the quantum depletion of the condensate, are exactly reproduced by Gross–Pitaevskii theory. Results are also given for the crossed particle-density response function and the extension of the formalism to nonuniform systems is discussed. The generalization of the Gross–Pitaevskii equation to include beyond mean field effects is finally considered and an explicit result for the chemical potential is found, in agreement with the prediction of Lee–Huang–Yang theory.