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 $N$.

arXiv comment59 pages

References in corpus (20)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• Ground State Energy of the Low Density Bose Gas
• The excitation spectrum for weakly interacting bosons in a trap
• The Excitation Spectrum for Weakly Interacting Bosons
• Quantitative Derivation of the Gross-Pitaevskii Equation
• Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• 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
• Bose particles in a box II. A convergent expansion of the ground state of the Bogoliubov Hamiltonian in the mean field limiting regime
• Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow
• Bose particles in a box III. A convergent expansion of the ground state of the Hamiltonian in the mean field limiting regime
• On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains

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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
• 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
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• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate