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

：陈旭文副教授
：2019-05-13 10:00
：实验楼105

       Speaker：Dr. Xuwen Chen

                        University of Rochester

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

       Time：13 May 2019,10:00

Location：实验楼105

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, 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.

      Speaker Introduction：陈旭文，博士，美国罗切斯特大学副教授（Tenured）。2012年美国马里兰大学获博士学位，2012年至2015年美国布朗大学从事博士后研究。陈旭文博士的研究方向为偏微分方程，论文发表在《Inventiones Mathematicae》、《Journal of the European Mathematical Society》、《Communications in Mathematical Physics》、《Archive for Rational Mechanics Analysis》等。

 联系人：  王焰金教授