# Central Limit Theorem for Bose-Einstein Condensates

## TL;DR

This paper proves that in a Bose gas trapped in a torus, the fluctuations of certain observables follow a normal distribution, demonstrating a central limit theorem in the ground state.

## Contribution

It establishes a central limit theorem for fluctuations of bounded one-particle observables in the ground state of a Bose gas in the Gross-Pitaevskii regime.

## Key findings

- Fluctuations satisfy a central limit theorem.
- Results apply to the ground state of the Bose gas.
- Validates normal distribution behavior of observables.

## Abstract

We consider a Bose gas trapped in the unit torus in the Gross-Pitaevskii regime. In the ground state, we prove that fluctuations of bounded one-particle observables satisfy a central limit theorem.