We report on analysis of the mode structure of a Bose-Einstein condensate loaded in a complex parabolic potential and subjected to a constant pump. Stationary solutions for the positive and negative scattering lengths are addressed. In the case of a positive scattering length and large number of atoms the ground state is described by the Thomas-Fermi distribution, whose properties in the presence of the dissipation are very different from its conservative counterpart. It is shown that for a positive scattering length only the ground state appears to be stable.
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Zezyulin et al. (2010) studied this question.
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