# Variance of a Trapped Bose-Einstein Condensate

## TL;DR

This paper investigates the behavior of a two-dimensional Bose-Einstein condensate's position variance, revealing anisotropic effects at many-body and mean-field levels despite full condensation and identical energies.

## Contribution

It demonstrates that the anisotropy of the position variance can differ between many-body and mean-field descriptions, even for a fully condensed system.

## Key findings

- Anisotropy of position variance can be opposite at many-body and mean-field levels.
- Energies per particle and densities per particle are identical at both levels.
- System remains 100% condensed despite variance anisotropy differences.

## Abstract

The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being $100\%$ condensed, and the respective energies per particle and densities per particle to coincide.