Off-diagonal long-range order in a harmonically confined two-dimensional Bose gas

Abstract

We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density martix provides an exact description of the spatial correlations known to be associated with the existence of a Bose-Einstein condensate below the transition temperature $T_c^{(0)}$. We treat the effects of repulsive interactions within the semiclassical Hartree-Fock-Bogliubov approximation and find that even though the system remains in the same {\em uncondensed phase} for all $T\ge 0$, there appears to be a revival of off-diagonal long-range order for temperatures $T<T_c^{(0)}$. We suggest that this reentrant order is related to a phase transition in the system which {\em is not} the BEC state.

figures embedded in text, typos corrected