Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime

Abstract

We consider Bose gases of $N$ particles in a box of volume one, interacting through a repulsive potential with scattering length of order $N^{1-\kappa }$, for $\kappa >0$. Such regimes interpolate between the Gross-Pitaevskii and thermodynamic limits. Assuming that $\kappa$ is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum of the system, up to errors vanishing in the limit of large $N$.

59 pages

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• 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
• Validity of Bogoliubov's approximation for translation-invariant Bose gases
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Beliaev damping in Bose gas
• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate