On two models of interacting Bose gas: Bogolyubov's model of superfluidity and Huang-Yang–Luttinger model

The equations for Green's functions are investigated and thermodynamically equivalent approximating Hamiltonians are derived for the model Hamiltonian of Bogolyubov's theory of superfluidity and the Huang-Yang–Luttinger (HYL) model Hamiltonian. The approximating Hamiltonians contain terms linear and quadratic in operators of creation and annihilation with momentum zero. On this basis, we prove that Bogolyubov's model describes superfluidity for certain values of the chemical potential, high densities, and low temperatures. It is shown that the expression for pressure derived in this paper for the HYL model coincides with that obtained earlier.