Exact diagonalization of the truncated Bogoliubov Hamiltonian

Abstract

The present short note is simply intended to communicate that I have analytically diagonalized the Bogoliubov truncated Hamiltonian $H_c$~\cite{Bogo1,Bogo2}, in an interacting bosonic gas. This is the natural prosecution of my work~\cite{MS}, now denoted as (I), where the diagonalization was performed only in the subspace corresponding to zero momentum collective excitations (CE).