Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron

TL;DR

This paper derives an optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron, confirming the classical effective mass and providing insights into the polaron's behavior at large coupling.

Contribution

It introduces a new upper bound for the polaron energy-momentum relation that is optimal in the strong coupling limit, matching the classical effective mass predictions.

Findings

Upper bound matches the two-term expansion for ground state energy at rest.

Quadratic term coefficient corresponds to inverse twice the classical effective mass.

Results validate classical effective mass predictions in the strong coupling regime.

Abstract

We consider the large polaron described by the Fr\"ohlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest, and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.