Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity

Abstract

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k=0 mode operator â0 is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is a gapless Bogolyubov spectrum of elementary excitations, leading to a proper microscopic interpretation of superfluidity.