We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius a/N, moving in the three-dimensional unit torus Λ. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N → ∞. 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.

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

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

Abstract

We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius a/N, moving in the three-dimensional unit torus Λ. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N → ∞. 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.
hard sphere bosons
ground state asymptotics
dilute bosons
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/24905
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