Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications

Lea Boßmann, Nikolai Leopold, David Mitrouskas, Sören Petrat

Published 2023-04-25Version 1

We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an Edgeworth expansion for fluctuations of one-body operators and the computation of the binding energy of an inhomogeneous Bose gas to any order. Finally, we collect related results for the dynamics of the weakly interacting Bose gas and for the regularized Nelson model.