Approximate Solutions of the Nonlinear Schr?dinger Equation for Ground and Excited States of Bose-Einstein Condensates |
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| Authors: | R. J. Dodd |
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| Affiliation: | National Institute of Standards and Technology, Gaithersburg, MD 20899-0001;Institute for Physical Science and Technology, University of Maryland at College Park, College Park, MD 20742 |
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| Abstract: | I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation. |
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| Keywords: | Bose-Einstein condensation, Ginzburg-Pitaevskii-Gross energy functional, Gross-Pitaevskii equation, mean-field theory, superfluidity, Thomas-Fermi functional model, time-independent nonlinear Schrö dinger equation, variational wave function, vortex formation |
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