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Chiara Saffirio - From the Many-Body Quantum Dynamics to the Vlasov Equation

Hausdorff Center for Mathematics via YouTube

Overview

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This course aims to teach the joint mean-field and semiclassical limit of the N-body Schrödinger dynamics leading to the Vlasov equation in the context of kinetic theory. The course covers topics such as derivation from an N-particle system, classical and quantum particles in mean-field regimes, effective equations, semiclassical limits, and specific mathematical transforms and estimates. The teaching method involves a lecture format, and the course is intended for individuals interested in many-body quantum dynamics and kinetic theory.

Syllabus

Intro
Derivation from N-particle system
Classical particles: mean-field regime
Classical particles: state of the art
Quantum particles: fermionic mean-field regime
Fermionic thean-field regime
Effective equation
State of art
Semiclassical limit
Weyl and Wigner transforms
Grönwall type estimate
Fefferman - de la Llave representation formula
Estimate on the dominant term
Remarks

Taught by

Hausdorff Center for Mathematics

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