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

2022/12/08 by Basti, Giulia, Cenatiempo, Serena, Giuliani, Alessandro +3 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.2212.04431

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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