The logarithmic term in the ground-state energy formula of a dilute fermi-gas of hard spheres

V Efimov

R. F. Bishop

P. Bocchieri, C. A. Orzalesi, V. H. Smith

P. Bocchieri, C. A. Orzalesi

Ludwig W. Bruch

Giulia Basti, Morris Brooks, Serena Cenatiempo +2 more

We consider a quantum gas consisting of $N$ hard spheres with radius $\frak{a} > 0$, obeying bosonic statistics and moving in the box $Λ= [0;L]^3$ with periodic boundary conditions. We are interested in the ground state energy per unit volume in the thermodynamic limit, with $N, L \to \infty$ at fixed density $ρ= N / L^3$. We derive an upper bound for the ground state energy density, matching the famous Lee-Huang-Yang formula, up to lower order terms, in the dilute limit $ρ\frak{a}^3 \ll 1$.