Abstract
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.
Schlein, Benjamin