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Stability of Attractive Bose–Einstein Condensates

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Abstract

We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein 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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-Ku, Tokyo, 153, Japan

    Jian Zhang

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  1. Jian Zhang
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Zhang, J. Stability of Attractive Bose–Einstein Condensates. Journal of Statistical Physics 101, 731–746 (2000). https://doi.org/10.1023/A:1026437923987

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