The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918386972229632 |
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| author | Basti, Giulia Brooks, Morris Cenatiempo, Serena Olgiati, Alessandro Schlein, Benjamin |
| author_facet | Basti, Giulia Brooks, Morris Cenatiempo, Serena Olgiati, Alessandro Schlein, Benjamin |
| contents | 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 $ρ\frak{a}^3 \ll 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13084 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound Basti, Giulia Brooks, Morris Cenatiempo, Serena Olgiati, Alessandro Schlein, Benjamin Mathematical Physics 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 $ρ\frak{a}^3 \ll 1$. |
| title | The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.13084 |