Semiclassical limit of polaron dynamics with cutoff

2025/09/24 by Gautier, Raphaël
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.20033

Abstract

We define and study the global well-posedness of a classical polaron dynamics and its derivation from the quantum dynamics of the Fröhlich Hamiltonian from the viewpoint of Wigner measures. We make a crucial use of the Gross transform, allowing us to extract a diverging constant. Finally, we discuss the difficulty of defining the classical dynamics when removing the cutoff in our setting.

Citations

• Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit
• Quantum-classical motion of charged particles interacting with scalar fields
• Mean square displacement of Brownian paths perturbed by bounded pair potentials
• Almost sure existence of global solutions for general initial value problems
• Almost Quartic Lower Bound for the Fröhlich Polaron's Effective Mass via Gaussian Domination
• The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
• Towards a derivation of Classical ElectroDynamics of charges and fields from QED
• Quasi-Classical Dynamics
• Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
• Mean field limit for bosons and infinite dimensional phase-space analysis

Related

• Monotonicity of the polaron energy
• A functional central limit theorem for Polaron path measures
• Convergence of states for polaron models in the classical limit
• Dyson expansion for form-bounded perturbations and applications to the polaron problem
• All-coupling solution for the continuous polaron problem in the Schrödinger representation