Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime

Abstract

We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $N^{-1+\kappa }$, for $\kappa >0$. Assuming that $\kappa \in (0;1/43)$, we show that low-energy states of the system exhibit complete Bose-Einstein condensation by providing explicit bounds on the expectation and on higher moments of the number of excitations.

69 pages + two appendices

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Cited by in corpus (26)

• 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
• A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
• The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime
• The Bose gas in a box with Neumann boundary conditions
• 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
• On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• 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
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• Lower bounds on the energy of the Bose gas
• On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
• Bose-Einstein condensation on hyperbolic spaces
• Friedrichs Diagrams -- Bosonic and Fermionic
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas
• Bogoliubov Transformations Beyond Shale-Stinespring: Generic $v^{\ast }v$ for bosons
• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate