Bogolyubov approximation for diagonal model of an interacting Bose gas

Abstract

We study, using the Bogolyubov approximation, the thermodynamic behaviour of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying $μ> λ(0)$, where $λ(0)\leq 0$ is the lowest energy value, the system undergoes Bose--Einstein condensation.