Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

The authors theoretically describe the stabilization of crystalline structures in interaction-driven Bose-Einstein condensates by analytically deriving a complex-valued Ginzburg-Landau equation for pattern formation. The resulting equation captures the competition between linear instability induced by the drive and nonlinear suppression induced by interactions and, in agreement with recent experiments, explains the emergence of square grid density patterns as stable states.