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

## TL;DR

This paper proves the existence of subsonic traveling waves in regularized Landau-Pekar equations and defines their effective mass.

## Contribution

A novel definition of effective mass is introduced and shown to align with existing low-energy definitions.

## Key findings

- Subsonic traveling waves exist in regularized Landau-Pekar equations with positive speed of sound.
- The effective mass is defined via energy-velocity expansion and matches energy-momentum expansion 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.

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Source: https://tomesphere.com/paper/PMC11379742