Derivation of an effective evolution equation for a strongly coupled polaron

TL;DR

This paper derives an effective nonlinear PDE that accurately describes the dynamics of a strongly coupled polaron, simplifying the quantum phonon interactions into a classical field approximation.

Contribution

It establishes a rigorous connection between the quantum polaron model and the classical Landau-Pekar equation in the strong coupling limit.

Findings

The effective equation accurately models polaron dynamics in the strong coupling regime.

The phonon field can be approximated as classical in this limit.

The derivation provides a rigorous foundation for the Landau-Pekar approximation.

Abstract

Fr\"{o}hlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron is approximated by an effective non-linear partial differential equation due to Landau and Pekar, in which the phonon field is treated as a classical field.