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The use of different complex scaling transformations for calculating the energies, chemical potentials, and tunneling lifetimes of trapped condensates are introduced [1,2].
For negative scattering lengths we show how within the framework of the Gross-Pitaevskii approximation, the transition from resonances to bound states takes place [1]. For positive scattering lengths we have managed to extract the fraction of particles which have tunneled through the potential barriers, as well as the maximal number of particles which can remain in the potential well, although the Gross-Pitaevskii equation does not give these informations directly [2]. References: [1] NM, L.D. Carr, B. A. Malomed, and Y. Band, J. Phys. B, 37, L193 (2004) [2] NM and L.S. Cederbaum, Los Alamos National Laboratory, Preprint Archive, Condensed Matter (2004), 1-11, arXiv:cond-mat/0406189. |