Asymptotic expansion of low-energy excitations for weakly interacting bosons

TL;DR

This paper develops an asymptotic expansion method for low-energy excitations in weakly interacting bosonic systems, providing higher-order corrections to Bogoliubov theory in the mean-field regime.

Contribution

It introduces a systematic approach to derive corrections to Bogoliubov theory for bosons with Coulomb interactions in the mean-field limit.

Findings

Derived asymptotic expansion for low-energy eigenstates and energies

Provides corrections to Bogoliubov theory to all orders in 1/N

Applicable to systems with Coulomb and similar interactions

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 $1/N$.