  We study quantum coherence properties of a dilute gas at temperatures above,
but not much above the transition temperature of Bose-Einstein condensation
(BEC). In such a gas, a small proportion of the atoms may possess coherence
lengths longer than the mean neighboring-atomic distance, implying the
existence of quantum coherence more than that expected for thermal atoms.
Conjecturing that a part of this proportion of the atoms may lie in a BEC-type
state, some unexplained experimental results [Phys. Rev. A, 71, 043615 (2005)]
can be explained.
