A simple 2nd order lower bound to the energy of dilute Bose gases

Abstract

For a dilute system of non-relativistic bosons interacting through a positive, radial potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho )\ge 4\pi a{\rho }^2(1-C\sqrt{\rho a^3})$.

arXiv comment27 pages. Enlarged class of allowed potentials. In particular the "hard core" is now covered

References in corpus (11)

• Ground State Energy of the Low Density Bose Gas
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Ground State Energy of the Two-Component Charged Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
• The ground state energy of the weakly interacting Bose gas at high density
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Ground State Energy of the One-Component Charged Bose Gas
• The Bogoliubov free energy functional II. The dilute limit
• The Bogoliubov free energy functional I. Existence of minimizers and phase diagram
• The Second Order Correction to the Ground State Energy of the Dilute Bose Gas

Cited by in corpus (11)

• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• Another proof of BEC in the GP-limit
• The Second Order Correction to the Ground State Energy of the Dilute Bose Gas
• The Bose gas in a box with Neumann boundary conditions
• Bogoliubov theory for dilute bose gases: the Gross-Pitaevskii Regime
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime