Variational solution of a superfluidity model

We derive, using the variational principle for the free energy, the solution of a model for superfluidity proposed in a previous paper. The solution has the phase diagram and the excitation spectrum expected from a superfluid. We draw the attention to the fact that the model is obtained, as compared with the Bogoliubov model, by a milder suppressing of interactions with the zero mode fluctuations, leading to the good spectral properties of superfluidity.