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

V.N. 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 $ρ\frak{a}^3 \ll 1$.