Beyond the dilute Bose gas

We discuss problems of three dimensional Bose gases in interaction but non-dilute. We then use the theory of a “weakly interacting” Bose gas recently analyzed as an attempt to obtain further insights into non-dilute systems. In particular, we develop the theory with additional remarks, discussions and a slight modification. The article concludes with a much more detailed analysis of the Bose condensate depletion, as well as a study of the two-fluid model of Tisza and Landau: the coexistence of normal and superfluid liquids at sufficiently low temperatures. In fact, even if it is based on one debatable hypothesis, this non-dilute gas qualitatively leads, up to Landau's “T4 law”, to a rigorous derivation of most of the previous theoretical studies on liquid helium. It also provides new observations, such as, for example, the coexistence of four subsystems of linked pair of particles: a thermal quasi-particle gas, a frozen jelly, a mixture between the previous ones, and a non-conventional Bose condensation of “Cooper-type pairs”. Moreover, the entropic gas is shown to be different from Landau's form associated with the normal liquid.