Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime

Abstract

We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Our work extends the previous results of Lieb, Seiringer and Yngvason on the leading order convergence, and of Boccato, Brennecke, Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of 'completing the square', inspired by recent works of Brietzke, Fournais and Solovej on the Lee-Huang-Yang formula, and a general estimate for Bogoliubov quadratic Hamiltonians on Fock space.

Final version to appear in Analysis & PDE

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Cited by in corpus (20)

• Bose-Einstein Condensation Beyond 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
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Another proof of BEC in the GP-limit
• The Bose gas in a box with Neumann boundary conditions
• The condensation of a trapped dilute Bose gas with three-body interactions
• Ground state energy of a Bose gas in the Gross-Pitaevskii regime
• 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
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• 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
• Bose-Einstein condensation on hyperbolic spaces
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime