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 matrix 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(0) c. We treat the effects of repulsive interactions within the semiclassical Hartree–Fock–Bogoliubov approximation and find that even though the system remains in the same uncondensed phase for all T≥0, there appears to be a revival of off-diagonal long-range order for temperatures T<T(0) c. We suggest that this re-entrant order is related to a phase transition in the system which is not the BEC state.
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