# Effective mass of the polaron -- revisited

## TL;DR

This paper investigates the energy-momentum relation of the Fröhlich polaron, establishing conditions under which the inverse effective mass is positive and coincides with the diffusion constant, with implications for polaron models across coupling regimes.

## Contribution

It combines spectral theory and the central limit theorem to analyze the effective mass of the polaron, extending results to models with ultraviolet cut-off and all coupling constants.

## Key findings

- Inverse effective mass is positive outside an intermediate coupling range.
- Inverse effective mass equals the diffusion constant.
- Results apply to polaron models with ultraviolet cut-off.

## Abstract

Properties of the energy-momentum relation for the Fr\"ohlich polaron are of continuing interest, especially for large values of the coupling constant. By combining spectral theory with the available results on the central limit theorem for the polaron path measure we prove that, except for an intermediate range of couplings, the inverse effective mass is strictly positive and coincides with the diffusion constant. Such a result is established also for polaron-type models with a suitable ultraviolet cut-off and for arbitrary values of the coupling constant. We point out a slightly stronger variant of the central limit theorem which would imply that the energy-momentum relation has a unique global minimum attained at zero momentum.