Focusing Dynamics of 2D Bose Gases in the Instability Regime

Explore the mathematical dynamics of two-dimensional Bose gases operating in the instability regime through this 24-minute conference talk. Examine the behavior of 2D Bose gases with interaction potentials of the form $N^{2 \beta-1} w\left(N^\beta \cdot\right)$ for $\beta \in(0,3 / 2)$, where negative and large interactions create instability conditions that may cause the corresponding focusing cubic nonlinear Schrödinger equation (NLS) to blow up in finite time. Learn how the $N$-body quantum dynamics can be effectively described by the NLS to leading order prior to the blow-up time, and discover the validity of the Bogoliubov approximation in capturing excitations from the condensate through norm approximation of many-body dynamics. Gain insights into collaborative research conducted with Lea Boßmann and Phan Thành Nam, presented during the thematic meeting on "Emergent phenomena in many-body quantum systems" at the Centre International de Rencontres Mathématiques in Marseille, France.