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Название: Stability of Attractive BoseEinstein Condensates
Автор: Zhang J.
We propose the critical nonlinear Schro dinger equation with a harmonic potential as a model of attractive BoseEinstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.