Upper bound for the ground state energy of a dilute Bose gas of hard spheres

2022/12/08 by Giulia Basti, Serena Cenatiempo, Basti, Giulia +9 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics

paper · doi:10.48550/arxiv.2212.04431

openalex publication_date 2022/12/08 · openalex created_date 2022/12/22 · openalex updated_date 2026/07/28

Abstract

We consider a gas of bosons interacting through a hard-sphere potential with radius \fraka 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 4πρ\fraka and shows that corrections are smaller than C ρ\fraka (ρ\fraka³)^1/2, for a sufficiently large constant C > 0. In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy is, in fact, of the order ρ\fraka (ρ\fraka³)^1/2, in agreement with the Lee-Huang-Yang prediction.

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