Asymptotic expansion of low-energy excitations for weakly interacting bosons

Abstract

We consider a system of $N$ bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in $1/N$.

62 pages; v3: this version appeared in Forum Math. Sigma; v2: revised and extended version

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• Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Weak Edgeworth expansion for the mean-field interacting Bose gas
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
• Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Beliaev damping in Bose gas
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• A Note on the Binding Energy for Bosons in the Mean-field Limit
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling
• Reduced fluctuations for bosons in a double well
• Low-energy spectrum and dynamics of the weakly interacting Bose gas