演讲人: 李用声 教授（华南理工大学）

题目：Derivation of the Nonlinear Schrodinger Equation From Quantum Many-Body Dynamics

摘要：the quantum many-body dynamics with m-body interactions in Λ = Rd or Λ = Td is considered.
This problem arises from the study of Bose-Einstein condensate (BEC). A Bose- Einstein condensate (BEC) is a peculiar gaseous state, a state of matter of a dilute gas of low densities (called bosons) cooled to temperatures very close to absolute zero (-273.15 ◦C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference, become apparent macroscopically. This state of matter can be used to explore fundamen- tal questions in quantum mechanics, such as the emergence of interference, decoherence, superfluidity and quantized vortices. Investigating various condensates has become one of the most active areas of contemporary research. A single particle in quantum mechanics is governed by a linear one-body Schro ̈dinger equation. If N bodies interact quantum mechanically, they are governed by the N-body linear Schro ̈dinger equation due to the superposition principle. Thus one arrive at the N-particle dynamic system for the anal- ysis of BEC, which is impossible to solve or simulate when N is large. Therefore, it is necessary to find reductions or approximations. It is long believed that NLS is the mean- field limit for these N-body systems. This has to be studied via rigorous mathematical proofs.

演讲人简介:华南理工大学数学学院教授，博士生导师，主要从事非线性发展程与无穷维动力系统的研究工作，主持5项国家自然科学基金及多项省部级基金，在国内外重要学术刊物如Annalesde l'Institut Henri Poincare, SIAM J. Math.Anal, J. Differential Equations等发表论文70余篇.

时间: 2019年9月28日 上午 10:30-12：00

地点: 数学中心 813