Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit

Abstract

We provide a rigorous derivation of the Landau-Pekar equations from the Fr\"ohlich Hamiltonian in the mean-field limit using Wigner measure techniques. On the classical side, we extend the global well-posedness results up to $L^2 \oplus L^2$. For obtaining the classical limit, we make a crucial use on the quantum side of the Gross transform, allowing us to study the system on the energy space, and with no ultraviolet cutoff.