Traveling waves and effective mass for the regularized Landau-Pekar equations

TL;DR

This paper establishes the existence of subsonic traveling waves in regularized Landau-Pekar equations with positive sound speed and introduces an effective mass concept consistent across different energy regimes.

Contribution

It provides a new definition of effective mass for these equations and proves its consistency with existing energy-momentum based definitions.

Findings

Existence of subsonic traveling waves in the equations.

A unified definition of effective mass.

Agreement between different effective mass definitions.

Abstract

We consider the regularized Landau-Pekar equations with positive speed of sound and prove the existence of subsonic traveling waves. We provide a definition of the effective mass for the regularized Landau-Pekar equations based on the energy-velocity expansion of subsonic traveling waves. Moreover we show that this definition of the effective mass agrees with the definition based on an energy-momentum expansion of low energy states.