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Two-Dimensional Gross-Pitaevskii Equation: Theory of Bose-Einstein Condensation and the Vortex State

Sang-Hoon Kim·Changyeon Won·Sung Dahm Oh·Wonho Jhe
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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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Sang-Hoon Kim, Changyeon Won, Sung Dahm Oh, Wonho Jhe. 1999-07-05. Two-Dimensional Gross-Pitaevskii Equation: Theory of Bose-Einstein Condensation and the Vortex State. https://arxiv.org/abs/cond-mat/9904087

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