# The energy of dilute Bose gases

## TL;DR

This paper rigorously proves the Lee-Huang-Yang formula for the ground state energy density of dilute Bose gases, confirming long-standing theoretical predictions through mathematical analysis.

## Contribution

It provides a rigorous mathematical proof of the Lee-Huang-Yang formula for dilute Bose gases' energy density, a key result in quantum many-body physics.

## Key findings

- Confirmed the Lee-Huang-Yang formula for energy density.
- Derived precise bounds for the ground state energy.
- Validated theoretical predictions with rigorous mathematics.

## Abstract

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.