Talk by François Golse (École Polytechnique, Paris)

Empirical Measures and Quantum Dynamics

The notion of phase-space empirical measure associated to a classical N-particle system, and its evolution under the dynamics defined by Newton's equations of motion, are a key ingredient in the derivation of the mean-field limit in classical mechanics. We define a quantum analogue of this notion of empirical measures and explain how it can be used to obtain a rate of convergence for the mean-field limit in quantum mechanics that is uniform in the Planck constant.
(Joint work with Thierry Paul.)