Dynamics of Bose–Einstein Condensation for Negative Scattering Length

Abstract. We investigate the dynamics of the trapped Gross-Pitaevskii equation, with negative two-body scattering length and nonconservative terms related to atomic feed-ing and nonlinear three-body recombination. Our aim is to explore the dynamics of collapses, that occurs in Bose-Einstein condensates of ultra-cold atoms, using a wide range of parameters for the nonconservative terms. A chaotic regime is found for cer-tain class of parameters, using a criterion proposed by Deissler et al. to characterize spatio-temporal chaos in nonlinear Schrödinger equations. The Bose-Einstein Condensation (BEC) of trapped dilute gas of 7Li atoms was observed experimentally by Hulet et al. [1], confirming a numerical simula-tion of Ruprecht et al. [2] for systems with negative two-body scattering length (a < 0). With the assumption of spherical symmetry, the condensate of such systems can be described by the following dimensionless generalization of the Gross-Pitaevskii equation: i ∂