A Note on the Binding Energy for Bosons in the Mean-field Limit

TL;DR

This paper derives an asymptotic expansion for the binding energy of weakly interacting bosons in the mean-field limit, confirming a conjecture and advancing understanding of bosonic gases and atoms.

Contribution

It provides the first explicit asymptotic expansion of the binding energy for bosonic gases, addressing a conjecture by Nam and extending to bosonic atoms.

Findings

Asymptotic expansion of binding energy derived

First orders explicitly computed for homogeneous gas

Addresses and confirms Nam's conjecture

Abstract

We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose-Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam [Lett. Math. Phys., 108(1):141--159, 2018], and provides an asymptotic expansion of the ionization energy of bosonic atoms.