AG Mathematische Physik, Lea Boßmann (FAU): Focusing dynamics for 2d Bose gases in the instability regime

Lea Boßmann (FAU)

Focusing dynamics for 2d Bose gases in the instability regime

Abstract:

We consider the dynamics of a 2d Bose gas with singular attractive
interactions in the instability regime, where the corresponding focusing
nonlinear Schrödinger equation (NLS) has a blow-up. We show that the
evolution of the condensate is effectively described by this NLS for all
times before the blow-up. Moreover, we prove the validity of the
Bogoliubov approximation for the fluctuation dynamics, resulting in a
norm approximation of the many-body dynamics. This is joint work with
Charlotte Dietze and Phan Thành Nam.