## Abstract

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

Original language | English |
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Article number | 1237 |

Number of pages | 16 |

Journal | Symmetry |

Volume | 13 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2021 |

### Bibliographical note

Funding Information:Funding: This research was funded by Israel Science Foundation (Grants No. 600/15 and 1516/19).

Publisher Copyright:

© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

## Keywords

- Angular-momentum variance
- Anisotropy
- Bose-Einstein condensates
- Harmonic-interaction model
- Infinite-particle-number limit
- Many-body theory
- Mean-field theory
- Momentum variance
- Position variance
- Solvable models

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)