A new microscopic theory of superfluidity for non-zero temperatures

The first microscopic theory of superfluidity was originally found in 1947 by Bogoliubov in three revolutionary papers on the theory of interacting Bose gas. His Weakly Imperfect Bose Gas (WIBG) coming from the truncation of a full interacting Bose gas was a starting point for this theory. However, only very few rigorous results concerning his WIBG and ansatzs were previously done until 1998-2000 where a first rigorous analysis of this Bogoliubov model (WIBG) was found at all temperatures and densities. The aim of this talk is to do a more deep analysis of the Bogoliubov theory, including all recent studies (2001) and some new criticizes (2002-2004). Actually, this more detailed analysis gives rise to a new microscopic theory of superfluidity at all temperatures (2004) then introduced at the end of this talk.

In particular, the talk should be concluded by the corresponding phase diagram of this new theory: it exhibits the ''Landau-type'' excitation spectrum in the presence of a depleted Bose condensation for small temperatures with the formation of "Cooper-type pairs", even at zero-temperature (experimentally, an estimate of the fraction of condensate in liquid $^{4}$He at T=0 K is $9$ $\%$).