Validity of Bogoliubov's approximation for translation-invariant Bose gases

Abstract

We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy $E_N$ is given by $E_N=N{e}_{\mathrm{H}}+\inf \sigma \left(\mathbb{H}\right)+o_{N\to \infty }(1)$, where $N$ is the number of particles, $e_{\mathrm{H}}$ is the minimal Hartree energy and $\mathbb{H}$ is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states ${\Psi }_N$, i.e. states satisfying $⟨H_N{⟩}_{{\Psi }_N}=E_N+o_{N\to \infty }(1)$, exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers.

References in corpus (2)

• Geometric methods for nonlinear many-body quantum systems
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime

Cited by in corpus (1)

• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy