Faraday patterns in Bose-Einstein condensates

A mechanism leading to spontaneous breaking of the space symmetry, and to the appearance of spatial patterns in the most recently created state of matter, the Bose-Einstein condensate (BEC), is proposed. The pattern formation are due to a periodic modulation in time of the scattering length of the condensed atoms. Experimentally this can be achieved via the Feshbach resonance, or, for low dimensional (1D or 2D) condensates, also by modulation of the trapping potential along a spatial coordinate normal to the "working" space. The parametric excitation of patterns in condensates by considering the mean-field Gross-Pitaevskii equation, and its dissipative generalization are investigated.