Almost Quartic Lower Bound for the Fr\"{o}hlich Polaron's Effective Mass via Gaussian Domination

Abstract

We prove the Fr\"{o}hlich polaron has effective mass at least $\frac{\alpha^4}{(\log \alpha)^6}$ when the coupling strength $\alpha$ is large. This nearly matches the quartic growth rate $C_*\alpha^4$ 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.