Faraday patterns in Bose-Einstein condensates. Amplitude equation for rolls in the parametrically driven, damped Gross-Pitaevskii equation
arXiv:cond-mat/0204406
Abstract
The parametrically driven, damped Gross-Pitaevskii equation, which models Bose-Einstein condensates in which the interatomic s-wave scattering length is modulated in time, is shown to support spatially modulated states in the form of rolls. A Landau equation with broken phase symmetry is derived, which governs the dynamics of the roll amplitude.