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

Brandon P. van Zyl
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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 $T^{(0)}_c$. 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 $T \geq 0$, there appears to be a revival of off-diagonal long-range order for temperatures $T < T^{(0)}_c$. We suggest that this reentrant order is related to a phase transition in the system which {\em is not} the BEC state.

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Brandon P. van Zyl. 2002-04-05. Off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. https://arxiv.org/abs/cond-mat/0204060

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