Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime

Abstract

We consider a Bose gas consisting of $N$ particles in ${\mathbb{R}}^3$, trapped by an external field and interacting through a two-body potential with scattering length of order $N^{-1}$. We prove that low energy states exhibit complete Bose-Einstein condensation with optimal rate, generalizing previous work in \cite{BBCS1, BBCS4}, restricted to translation invariant systems. This extends recent results in \cite{NNRT}, removing the smallness assumption on the size of the scattering length.

arXiv comment67 pages

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• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
• On Bose-Einstein condensates in the Thomas-Fermi regime
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• Reduced fluctuations for bosons in a double well
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators