Two-Dimensional Gross-Pitaevskii Equation: Theory of Bose-Einstein Condensation and the Vortex State
Abstract
We derive the Gross-Pitaevskii equation in two-dimension from the first principles of two-dimensional scattering theory. Numerical calculation of the condensate wave function shows that atoms in a two-dimensional harmonic trap can be condensed into its ground state. Moreover, the ground state energy and the wave function of two-dimensional vortex state are also obtained. Quantitative comparisons between 2D results and 3D ones are made in detail.
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