# A simple upper bound for the ground state energy of a dilute Bose gas of hard spheres

Giulia Basti, Serena Cenatiempo, Alessandro Giuliani, Alessandro Olgiati, Giulio Pasqualetti, Benjamin Schlein

Giulia Basti, Serena Cenatiempo, Alessandro Giuliani, Alessandro Olgiati, Giulio Pasqualetti, Benjamin Schlein

**8/12/22**Published in : arXiv:2212.04431

We consider a gas of bosons interacting through a hard-sphere potential with radius \frak{a} in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the leading term 4\pi \frak{a} \rho and shows that corrections are of order smaller than \rho \frak{a} (\rho \frak{a}^3)^{1/2-\epsilon}, for any \epsilon > 0.