Global Derivation of the 1D Vlasov-Poisson Equation from Quantum Many-body Dynamics
数学专题报告
报告题目(Title)：Global Derivation of the 1D Vlasov-Poisson Equation from Quantum Many-body Dynamics
报告人(Speaker)：陈旭文 教授 （Rochester大学）
地点(Place)：后主楼1225
时间(Time)：2025年5月13日周二 16:00-17:00
邀请人(Inviter)：袁迪凡
报告摘要
We study the 1D quantum many-body dynamics with a screened Coulomb potential in the mean-field setting. Combining the quantum mean-field, semiclassical, and Debye length limits, we prove the global derivation of the 1D Vlasov-Poisson equation. We tackle the difficulties brought by the pure state data, whose Wigner transforms converge to Wigner measures. We find new weighted uniform estimates around which we build the proof. As a result, we obtain, globally, stronger limits, and hence the global existence of solutions to the 1D Vlasov-Poisson equation subject to such Wigner measure data, which satisfy conservation laws of mass, momentum, and energy, despite being measure solutions. This happens to solve, even with general data, the 1D measure solution case of an open problem regarding the conservation law of the Vlasov-Poisson equation raised by Diperna and Lions.
主讲人简介
陈旭文教授，美国罗切斯特大学数学系教授，西蒙斯学者奖获得者，长期获得美国国家科学基金会（NSF）资助，主要从事量子多体问题、动理学方程等领域的偏微分方程的数学理论研究，学术成果发表于 Inventiones Mathematicae, Forum of Mathematics PI, Journal of the European Mathematical Society, Peking Mathematical Journal, Annals of PDE, Archive for Rational Mechanics and Analysis, Communications in Mathematical Physics 等国际顶级期刊。
