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

Abstract

We prove the Fröhlich 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 $C_{\ast }{\alpha }^4$ 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.