The effective mass problem for the Landau-Pekar equations

TL;DR

This paper introduces a new variational approach to define the effective mass of a classical polaron within the Landau-Pekar framework, aligning with traditional predictions and providing a rigorous mathematical foundation.

Contribution

It presents a novel variational principle for defining the polaron's effective mass, based on energy minimization with fixed initial velocity, confirming Landau and Pekar's earlier predictions.

Findings

The effective mass formula matches Landau and Pekar's prediction.

A new variational principle for the classical polaron is established.

The approach provides a rigorous mathematical foundation for the effective mass concept.

Abstract

We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar [10].