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

2025/09/24 by Gautier, Raphaël · 1 citation
Mathematics · Physics and Astronomy · Computer Science · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum Information and Cryptography

paper · pdf · doi:10.48550/arxiv.2509.20043

Abstract

We provide a rigorous derivation of the Landau-Pekar equations from the Fröhlich Hamiltonian in the mean-field limit using Wigner measure techniques. On the classical side, we extend the global well-posedness results up to L² ⊕ 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.

Citations

• Quantum-classical motion of charged particles interacting with scalar fields
• Mean square displacement of Brownian paths perturbed by bounded pair potentials
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• The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
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• Quasi-Classical Dynamics
• Mean field propagation of infinite dimensional Wigner measures with a\n singular two-body interaction potential
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• Mean field limit for bosons and infinite dimensional phase-space analysis
• Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

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