A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime

Abstract

We prove an upper bound for the ground state energy of a Bose gas consisting of $N$ hard spheres with radius $\mathfrak{a}/N$, moving in the three-dimensional unit torus $\Lambda$. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit $N\to \infty$. The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose-Einstein condensate and describing correlations on large scales.

Final version, 58 pages

References in corpus (3)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime

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• 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
• Lower bounds on the energy of the Bose gas
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime