# A simple 2nd order lower bound to the energy of dilute Bose gases

## TL;DR

This paper establishes a simple lower bound on the ground state energy density of dilute Bose gases, improving understanding of their energetic properties in quantum many-body physics.

## Contribution

It provides a new, straightforward second-order lower bound on the energy of dilute Bose gases, refining previous estimates and aiding theoretical analysis.

## Key findings

- Proves a lower bound: $e(
ho) \,\geq\, 4\pi a \rho^2 (1 - C \sqrt{\rho a^3})$
- Validates the bound for systems with positive, radial interaction potentials
- Enhances theoretical understanding of dilute Bose gas energetics

## Abstract

For a dilute system of non-relativistic bosons interacting through a positive, radial potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1- C \sqrt{\rho a^3} \,)$.