Order Parameter, Mean-Field Theory, and the Ideal Bose Gas

Publisher Website
Google Scholar
Abstract
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.