报告人：陈旭文(University of Rochester)
时 间：2019年5月15日 下午15:00-16:00
地点：华南数学应用与交叉研究中心学术报告厅111
题目：The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
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, 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 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 use it to prove a new type of uniqueness theorem.