数学物理及偏微分方程国际系列论坛（9）：Focusing dynamics of 2D Bose gases

发布时间：2024-09-14 作者：浏览次数：

Speaker:	Professor Phan Thanh Nam, LMU Munich (Germany)	DateTime:	Beijing Time: 16: 30--17: 30, September 17 (Tuesday), 2024
Brief Introduction to Speaker: Phan Thanh Nam现为德国慕尼黑大学教授。主要从事偏微分方程分析、数学物理、变分理论等领域的理论研究，特别是在多体量子力学等领域做出过具有国际影响力的系列研究成果，在Invent. Math.、CPAM、JEMS等国际顶尖数学期刊上发表论文60余篇，现为Mathematische Zeitschrift等国际数学杂志编委。		Place:	Zoom Meeting ID: 483 184 2093, Passcode: 2024
Abstract:We consider the dynamics of a Bose gas in 2D, described by a many-body Schrödinger equation with a mean-field type interaction potential. The interaction can be chosen to be negative and large, leading to an instability regime where the corresponding focusing cubic nonlinear Schrödinger equation (NLS) may blow up in finite time. We show that, to leading order, the many-body quantum dynamics can be effectively described by the NLS prior to the blow-up time. This is achieved through a rigorous justification of the Bogoliubov approximation on the excitations around the Bose-Einstein condensate. This is joint work with Lea Bossmann and Charlotte Dietze.