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

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.