# The Landau-Pekar equations: Adiabatic theorem and accuracy

## TL;DR

This paper proves an adiabatic theorem for the Landau-Pekar equations, demonstrating their accuracy as effective models for the Fröhlich Hamiltonian's evolution with large coupling, especially for short timescales.

## Contribution

It establishes an adiabatic theorem for the Landau-Pekar equations and quantifies their accuracy in approximating the Fröhlich Hamiltonian dynamics.

## Key findings

- Landau-Pekar equations accurately approximate the Fröhlich Hamiltonian for short times.
- The adiabatic theorem provides bounds on the approximation error.
- Effective equations are valid until timescales short compared to α^2.

## Abstract

We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fr\"ohlich Hamiltonian with large coupling constant $\alpha$. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau-Pekar equations until times short compared to $\alpha^2$.