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arXiv · 2203.11917

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

Giulia Basti·Serena Cenatiempo·Alessandro Olgiati·Giulio Pasqualetti·Benjamin Schlein
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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.

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Giulia Basti, Serena Cenatiempo, Alessandro Olgiati, Giulio Pasqualetti, Benjamin Schlein. 2022-03-22. A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime. https://doi.org/10.1007/s00220-022-04547-y

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