A new microscopic theory of superfluidity at all temperatures

Following the program suggested in [1], we propose a new microscopic theory of superfluidity for all temperatures and densities. In particular, the corresponding phase diagram of this theory exhibits: (i) a thermodynamic behavior corresponding to the Perfect Bose Gas for small densities or high temperatures, (ii) the "Landau-type" excitation spectrum in the presence of non-conventional Bose condensation for high densities or small temperatures, (iii) a depletion of the Bose condensate with the formation of "Cooper-type pairs", even at zero-temperature (experimentally, an estimate of the fraction of condensate in liquid He-4 at T=0 K is 9%, see [2,3]). In contrast to Bogoliubov's last approach and while warning that the full interacting Hamiltonian is truncated, the analysis performed here is rigorous by involving a complete thermodynamic analysis of a non-trivial continuous gas in the canonical ensemble.