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arXiv · 2202.12294

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

Christian Brennecke
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Abstract

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.

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Christian Brennecke. 2022-02-24. The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. https://doi.org/10.1063/5.0089630

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