Renewal approach for the energy-momentum relation of the Fr\"ohlich polaron

TL;DR

This paper investigates the energy-momentum relation of the Fröhlich polaron, demonstrating its non-decreasing nature, negative correction to quasi-particle energy, and that the effective mass exceeds one, without relying on a central limit theorem.

Contribution

It introduces a renewal approach to analyze the polaron's energy-momentum relation, providing new proofs and insights into its properties.

Findings

Energy-momentum relation is non-decreasing.

Correction to quasi-particle energy is negative.

Effective mass exceeds one, lying in (1, ∞).

Abstract

We study the qualitative behaviour of the energy-momentum relation of the Fr\"ohlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is negative. We give a proof that the effective mass lies in $(1, \infty)$ that does not need the validity of a central limit theorem for the path measure.