Gross–Pitaevskii Evolution for Bose–Einstein condensates

In these notes, we review the results of the paper Gross–Pitaevskii dynamics for Bose–Einstein condensates, a joint work with C. Brennecke. We consider the time evolution of initially trapped Bose–Einstein condensates, in a scaling limit where the interaction has a small scattering length. We show that the condensation is preserved by the many-body dynamics and that the evolution of the condensate wave function is governed by the nonlinear Gross–Pitaevskii equation. Compared with previous results, we prove here the convergence with optimal rates