Colloquia

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. In this talk I will show that for short-ranged repulsive interactions this theory fails in one and two spatial dimensions, and appropriate low-dimensional modifications will be proposed. The new theory has a universal character, and some of its implications such as density profiles in confining potentials, superfluidity, solitons, and self-similar solutions will be discussed.