标题： Wigner测度方法在平均场极限下推导Landau-Pekar方程 显示英文标题

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

摘要： 我们使用Wigner测度技术，从平均场极限中的Fröhlich哈密顿量严格推导出Landau-Pekar方程。在经典方面，我们将全局适定性结果扩展到$L^2 \oplus L^2$。为了获得经典极限，我们在量子方面关键地使用了Gross变换，使我们能够在能量空间上研究系统，并且无需紫外截断。 显示英文摘要

摘要： 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.