Norm Approximation of Bosonic Mean-Field Dynamics by Quasifree Evolution

In this talk, I will consider the quantum many-body evolution of a homogeneous Bose gas in three dimensions in the mean-field scaling regime. I will study a class of initial data describing finitely many excitations over a quasi-stationary Bose-Einstein condensate. Using a rigorous version of Bogolyubov's theory, I will prove that the many-body evolution can be approximated in Fock space norm by a quasifree bosonic evolution of the excitations with an error which grows linearly in time. This talk is based on an ongoing work with Chiara Boccato (University of Pisa).