Linking classical and quantum time evolution with measure theoretical tools

par Raphaël Gautier (Université de Rennes)

jeudi 12 mars 2026, 14:00 → 16:00 Europe/Paris

Pellos (1R2 second floor)

Semiclassical analysis studies how quantum mechanics reproduces classical mechanics in the regime where the Planck constant is small. In this talk, I will present how it is possible to link the quantum evolution (governed by Schrödinger's equation) to the classical evolution (governed by Newton's equation), in the simplest case of one particle with potential energy V(x). I will first recall the mathematical formulation of quantum mechanics, then define the semiclassical measure of a quantum state via a Fourier type transform, and finally present the scheme of the proof of the link between the two evolutions. The key steps will be to take the limit in a Duhamel type formula, to then obtain a solvable transport equation solved by the semiclassical measures.