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arXiv · 2307.00956

Focusing dynamics of 2D Bose gases in the instability regime

Lea Boßmann·Charlotte Dietze·Phan Thành Nam
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Abstract

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 Schr{\"o}dinger 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.

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Lea Boßmann, Charlotte Dietze, Phan Thành Nam. 2023-07-03. Focusing dynamics of 2D Bose gases in the instability regime. https://arxiv.org/abs/2307.00956

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