Orateur
Charlotte Dietze
Description
We consider the dynamics of a 2D Bose gas with an interaction
potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$.
The interaction may be chosen to be negative and large, leading to the
instability regime where the corresponding focusing cubic nonlinear
Schrödinger equation (NLS) may blow up in finite time. We show that to
leading order, the $N$-body quantum dynamics can be effectively described by
the NLS prior to the blow-up time. Moreover, we prove the validity of the
Bogoliubov approximation, where the excitations from the condensate are
captured in a norm approximation of the many-body dynamics. This is joint work with Lea Boßmann and Phan Thành Nam.
