12-24【Xuwen Chen】五教5207 偏微分方程讨论班系列报告


Title:The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics

Speaker:Professor Xuwen Chen    (University of Rochester)

Time:2019年12 月24日        下午    14:00-15:00

Room:东区第五教学楼  5207教室

Abstract: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.

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