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-Pitaevskii limit. Here, we only sketch the main ideas, details will appear elsewhere.

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

Giulia Basti
Membro del Collaboration Group
;
Serena Cenatiempo
Membro del Collaboration Group
;
2022

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-Pitaevskii limit. Here, we only sketch the main ideas, details will appear elsewhere.
Interacting bosons
hard sphere interaction
Gross-Pitaevekii regime
Lee-Huang-Yang asymptotics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/24904
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