Exact diagonalization of the truncated Bogoliubov Hamiltonian

TL;DR

This paper analytically diagonalizes the truncated Bogoliubov Hamiltonian for an interacting bosonic gas, extending previous work that focused only on zero momentum collective excitations, providing a more complete understanding of the system.

Contribution

It provides the first exact analytical diagonalization of the full truncated Bogoliubov Hamiltonian, advancing the theoretical understanding of interacting bosonic gases.

Findings

Analytical diagonalization of the full truncated Hamiltonian achieved

Extension of previous zero-momentum results to full spectrum

Enhanced theoretical framework for bosonic gas interactions

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).