Bose particles in a box II. A convergent expansion of the ground state of the Bogoliubov Hamiltonian in the mean field limiting regime

Abstract

In this paper we consider an interacting Bose gas at zero temperature, in a finite box and in the mean field limiting regime. The N gas particles interact through a pair potential of positive type and with an ultraviolet cut-off. Its (nonzero) Fourier components are sufficiently large with respect to the corresponding kinetic energies of the modes. Using the multi-scale technique in the occupation numbers of particle states introduced in [Pi1], we provide a convergent expansion of the ground state of the particle number preserving Bogoliubov Hamiltonian in terms of the bare operators. In the limit N \to \infty the expansion is up to any desired precision.

Small modifications in Corollary 5.1. A "supporting file" section at the end of the manuscript contains some lengthy computations related to the proofs

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• The ground state energy of the weakly interacting Bose gas at high density
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Cited by in corpus (10)

• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Beyond Bogoliubov Dynamics
• Bose particles in a box I. A convergent expansion of the ground state of a three-modes Bogoliubov Hamiltonian
• Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Bogoliubov theory for dilute bose gases: the Gross-Pitaevskii Regime
• Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
• Analysis of fluctuations around non linear effective dynamics
• Low-energy spectrum and dynamics of the weakly interacting Bose gas