Almost quartic lower bound for the Fröhlich polaron’s effective mass via Gaussian domination

Abstract

We prove that the Fröhlich polaron has effective mass at least $\frac{{\mathit{\alpha }}^4}{{(log\mathit{\alpha })}^6}$ when the coupling strength α is large. This nearly matches the quartic growth rate $C_{\ast }{\mathit{\alpha }}^4$ predicted by Landau and Pekar, and complements a recent sharp upper bound proved by Brooks and Seiringer. Our proof works with the path integral formulation of the problem and systematically applies the Gaussian correlation inequality to exploit quasiconcavity of the interaction terms.