Effective mass of the Polaron: a lower bound

TL;DR

This paper establishes a lower bound on the effective mass of the Fröhlich Polaron, demonstrating it grows at least as fast as a constant times the coupling constant to the power of 2/5, using a novel path measure approach.

Contribution

It provides the first rigorous lower bound on the polaron's effective mass that applies for all coupling strengths, using the point process representation.

Findings

Effective mass is bounded below by c*α^{2/5}.

The proof employs the point process representation of the path measure.

The result holds for all coupling constants α.

Abstract

We show that the effective mass of the Fr\"ohlich Polaron is bounded below by $c\alpha^{2/5}$ for some constant $c>0$ and for all coupling constants $\alpha$. The proof uses the point process representation of the path measure of the Fr\"ohlich Polaron.