Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates
arXiv:cond-mat/0405064 · doi:10.1103/PhysRevA.70.023602
Abstract
This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to ``engineer'' the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior.
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