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Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit (2509.20043v1)
Published 24 Sep 2025 in math-ph, math.AP, and math.MP
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 $L2 \oplus L2$. 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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