Speaker: 何凌冰教授，清华大学

Inviter: 王勇研究员

Title: Derivation of the Fokker-Planck-Landau Equation from the Quantum Boltzmann Equation via Semi-Classical Limit

Language: Chinese

Time & Venue: 2025.02.21 14:00-15:00 思源楼813

Abstract: It is widely accepted that in the weak coupling regime, the Fokker-Planck-Landau equation is the primary effective model for charged particles. This talk aims to support this assertion by deriving the Fokker-Planck-Landau equation from the quantum Boltzmann equation using a semi-classical limit. We approach this derivation in two distinct contexts:

1) Weak Convergence of Solutions: We demonstrate that the weak solutions of the Boltzmann equation converge weakly to the H-solution of the Landau equation for any radical initial data.

2) Asymptotic Expansion: We establish an asymptotic expansion formula that describes the limiting behavior for a short time with regular initial data.

Through these analyses, we provide a comprehensive framework linking the quantum Boltzmann equation to the Fokker-Planck-Landau equation, reinforcing its significance as a fundamental model in the study of charged particle dynamics in weakly interacting systems.