Ground state energy of a Bose gas in the Gross-Pitaevskii regime

Abstract

We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson's upper bound, which provides the correct leading order asymptotics for hard spheres. Afterwards, we discuss a rigorous version of Bogoliubov theory, which recently led to an estimate for the ground state energy in the Gross-Pitaevskii regime, valid up to second order, for particles interacting through integrable potentials. Finally, we explain how these ideas can be combined to establish a new upper bound, valid to second order, for the energy of hard spheres in the Gross-Pitaeavskii limit. Here we only sketch the main ideas, details will appear elsewhere.

Postprint version. To appear in JMP

References in corpus (5)

• 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
• 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

Cited by in corpus (2)

• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• Reduced fluctuations for bosons in a double well