Kolloquium GRK 2339, Prof. L. Boßmann

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.