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The Two-Dimensional Bose-Einstein Condensate

Juan Pablo Fernandez·William J. Mullin
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Abstract

We study the Hartree-Fock-Bogoliubov mean-field theory as applied to a two-dimensional finite trapped Bose gas at low temperatures and find that, in the Hartree-Fock approximation, the system can be described either with or without the presence of a condensate; this is true in the thermodynamic limit as well. Of the two solutions, the one that includes a condensate has a lower free energy at all temperatures. However, the Hartree-Fock scheme neglects the presence of phonons within the system, and when we allow for the possibility of phonons we are unable to find condensed solutions; the uncondensed solutions, on the other hand, are valid also in the latter, more general scheme. Our results confirm that low-energy phonons destabilize the two-dimensional condensate.

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Juan Pablo Fernandez, William J. Mullin. 2002-05-20. The Two-Dimensional Bose-Einstein Condensate. https://arxiv.org/abs/cond-mat/0203175

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