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arXiv · 2509.20043

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

Raphaël Gautier
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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.

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Raphaël Gautier. 2025-09-24. Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit. https://arxiv.org/abs/2509.20043

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