# Mid-range order in trapped quasi-condensates of bosonic atoms

## TL;DR

This paper investigates mid-range order in finite trapped Bose systems, demonstrating that quasi-condensates exhibit properties close to true condensates and can be characterized by order indices of density matrices.

## Contribution

It introduces a method to characterize mid-range order in finite Bose systems using order indices of density matrices, advancing understanding of quasi-condensates.

## Key findings

- Quasi-condensates exhibit mid-range order similar to true condensates.
- Order indices effectively characterize the level of order in finite Bose systems.
- Finite Bose systems can display properties close to genuine Bose-Einstein condensation.

## Abstract

Finite Bose systems cannot display a genuine Bose-Einstein condensate with infinite long-range order. But, if the number of trapped atoms is sufficiently large, a kind of Bose-Einstein condensation does occur, with the properties of the arising quasi-condensate being very close to the genuine condensate. Although the quasi-condensate does not enjoy long-range order, it has mid-range order. This paper shows that the level of mid-range order in finite Bose systems can be characterized by order indices of density matrices.