The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
报告题目(Title)：The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
报告人(Speaker)：Xuwen Chen （University of Rochester）
地点(Place)：后主楼1124
时间(Time)：2019年6月18日下午午4:00-5:00
邀请人(Inviter)：薛庆营
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.
