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arXiv · 2603.13084

The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound

Giulia Basti·Morris Brooks·Serena Cenatiempo·Alessandro Olgiati·Benjamin Schlein
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Abstract

We consider a quantum gas consisting of $N$ hard spheres with radius $\frak{a} > 0$, obeying bosonic statistics and moving in the box $\Lambda = [0;L]^3$ 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 $\rho = N / L^3$. 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 $\rho \frak{a}^3 \ll 1$.

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Giulia Basti, Morris Brooks, Serena Cenatiempo, Alessandro Olgiati, Benjamin Schlein. 2026-03-13. The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound. https://arxiv.org/abs/2603.13084

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