For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+ \frac{128}{15\sqrt{\pi}} \sqrt{\rho a^3} +o(\sqrt{\rho a^3}\,))$, thereby proving the Lee-Huang-Yang formula for the energy density.

中文翻译：

---

稀释玻色气体的能量

对于通过正 $L^1$ 势 $v$ 与散射长度 $a$ 相互作用的非相对论玻色子的稀释系统，我们证明基态能量密度满足边界 $e(\rho) \geq 4\pi一个 \rho^2 (1+ \frac{128}{15\sqrt{\pi}} \sqrt{\rho a^3} +o(\sqrt{\rho a^3}\,))$，从而证明能量密度的 Lee-Huang-Yang 公式。