(Lecture) Optimal Transport Distances in Quantum Mechanics

Abstract: The first part of this talk is focussed on the definition of an extension of the Monge-Kantorovich-Wasserstein distance of exponent 2 to the set density operators, which correspond to probability measures in quantum mechanics. We shall mostly explore the metric properties of this extension, in particular compare it with the Wasserstein metric itself, and discuss variants of the triangle inequality.

The second part of the talk presents some applications of this notion of quantum Wasserstein distances, to the uniform convergence of time-splitting schemes in the Planck constant for quantum dynamics, to effective observation inequalities for the Heisenberg or the Schrödinger equations, and to the uniformity in the Planck constant of convergence rates for the mean-field limit in quantum mechanics. (Based on a series of works with E. Caglioti, C. Mouhot and T. Paul)

analysis of PDEs

Audience: researchers in the topic

Open PDE and analysis seminar and lectures