Almost Quartic Lower Bound for the Fröhlich Polaron's Effective Mass via Gaussian Domination

2022/12/28 by Mark Sellke, Sellke, Mark · 2 citations
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2212.14023

openalex publication_date 2022/12/28 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

Abstract

We prove the Fröhlich polaron has effective mass at least (α⁴)/((log α)⁶) when the coupling strength α is large. This nearly matches the quartic growth rate C_*α⁴ predicted by Landau and Pekar in 1948 and complements a recent sharp upper bound of Brooks and Seiringer. Our proof works with the path integral formulation of the problem and systematically applies the Gaussian correlation inequality to exploit quasi-concavity of the interaction terms.

Cited by

• Semiclassical limit of polaron dynamics with cutoff
• Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit

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