The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
Speaker :
Time :
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Title: The Derivation of the Energy-critical NLS from QuantumMany-body Dynamics
Speaker: Professor Xuwen Chen(University of Rochester)
Time：2018.12.17 11:00-12:00
Location: 105, gongshangbuilding
Abstract: We derive the 3Denergy critical quintic NLS from quantum many-body dynamics with 3-bodyinteraction in the T^3 (periodic) setting. Due to the known complexity of theenergy critical setting, previous progress was limited in comparison to the2-body interaction case yielding energy subcritical cubic NLS. We developmethods to prove the convergence of the BBGKY hierarchy to the infiniteGross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GPsolutions. Since the trace estimate used in the previous proofs of convergenceis the false sharp trace estimate in our setting, we instead introduce a newfrequency interaction analysis and apply the finite dimensional quantum deFinetti theorem. For the large solution uniqueness argument, we discover thenew HUFL (hierarchical uniform frequency localization) property for the GPhierarchy and use it to prove a new type of uniqueness theorem.