Low-dimensional bose liquids: beyond the gross-pitaevskii approximation
The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d</=2, and we propose the appropriate low-dimensional modifications, which have a universal form. For d = 1 we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.
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