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

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.

Contribution to the Proceedings of ICMP 2021, 17 pages

References in corpus (9)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Another proof of BEC in the GP-limit
• On Bose-Einstein condensates in the Thomas-Fermi regime
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger

Cited by in corpus (1)

• Reduced fluctuations for bosons in a double well