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arXiv · 2108.12022

The energy of dilute Bose gases II: The general case

Soeren Fournais·Jan Philip Solovej
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Abstract

For a dilute system of non-relativistic bosons interacting through a positive potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(ρ) \geq 4πa ρ^2 (1+ \frac{128}{15\sqrtπ} \sqrt{ρa^3} +o(\sqrt{ρa^3}\,))$, thereby proving a lower bound consistent with the Lee-Huang-Yang formula for the energy density. The proof allows for potentials with large $L^1$-norm, in particular, the case of hard core interactions is included. Thereby, we solve a problem in mathematical physics that had been a major challenge since the 1960's.

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Soeren Fournais, Jan Philip Solovej. 2021-11-06. The energy of dilute Bose gases II: The general case. https://arxiv.org/abs/2108.12022

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