学术报告报告题目：The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
报 告 人：陈旭文 副教授（美国罗切斯特大学）
报告时间：2018年12月10日（星期一）下午16:30-17:30
报告地点：4号楼318室
邀 请 人：李用声 教授
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数学学院
2018年12月4日
报告摘要：
We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem.
报告人简介：
陈旭文，2012年博士毕业于美国马里兰大学，师从数学家Manoussos Grillakis and Matei Machedon，现任美国罗切斯特大学副教授。从事量子多体问题和非线性Schrodinger的研究工作。