The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime

Bogoliubov Theory provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov’s predictions could be justified rigorously in \cite{BBCS3} for translation invariant systems in the Gross-Pitaveskii regime, where $N$ bosons in $\Lambda = [0;1]^3\subset $\mathbb{R}$^3$ interact through a potential whose scattering length is of size $N^{-1}$. In this note, we review recent results from \cite{BSS2}, a joint work with B. Schlein and S. Schraven, which extends the analysis of \cite{BBCS3} to systems of bosons in ${\mathbb{R}}^3$ that are trapped by an external potential.