中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Phan Thanh Nam (Mathematics Institute, LMU Munich)
题 目：Random phase approximation for the mean-field electron gas （1）
时 间：2023.11.20（星期一）16:00-17:00
地 点：Meeting ID: 924 888 5804 Passcode: AMSS2022
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题 目：Random phase approximation for the mean-field electron gas （2）
时 间：2023.11.21（星期二）16:00-17:00
地 点：Meeting ID: 924 888 5804 Passcode: AMSS2022
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题 目：Random phase approximation for the mean-field electron gas （3）
时 间：2023.11.22（星期三）16:00-17:00
地 点：Meeting ID: 924 888 5804 Passcode: AMSS2022
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题 目：Random phase approximation for the mean-field electron gas （4）
时 间：2023.11.24（星期五）16:00-17:00
地 点：Meeting ID: 924 888 5804 Passcode: AMSS2022
摘 要：Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While the microscopic derivation of the RPA has included notable work by theoretical physicists since the 1950s, the mathematical justification remains very challenging due to the failure of second-order perturbation theory. In this course, I will discuss recent developments concerning the mathematical understanding of the RPA in the mean-field regime. Starting from first principles of quantum mechanics, I will explain the validity of the PRA in predicting the correlation energy and the elementary excitation spectrum of a class of weakly interacting fermionic systems, including the Coulomb gas. This is based on a rigorous bosonization method where suitable pairs of fermions are interpreted as bosons in an appropriate sense, resulting an effective Hamiltonian which can be diagonalized explicitly by Bogoliubov's method.
个人简介：Phan Thành Nam is a Professor at the Department of Mathematics at LMU Munich. His research field is analysis and mathematical physics, in particular in many-body quantum mechanics, spectral theory, calculus of variations and partial differential equations and numerical analysis.
Previously, he was an Assistant Professor at the Masaryk University and an IST Fellow at the Institute of Science and Technology in Austria. He has twice been an invited speaker at the International Congress on Mathematical Physics (ICMP). In 2018, he was awarded the IUPAP Young Scientist Prize in Mathematical Physics for young researchers who perform original work of outstanding scientific quality in mathematical physics. Recently, he is EMS Prize winner in 2020.
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