On the dynamics of polarons in the strong-coupling limit

TL;DR

This paper derives a nonlinear Schr"odinger-Poisson system from the Fr"ohlich polaron model in the strong-coupling limit, using variational principles, and analyzes the accuracy of these solutions for polaron dynamics, extending results to multiple polarons.

Contribution

It introduces a derivation of the Schr"odinger-Poisson system from the Fr"ohlich model and provides new insights into the accuracy of these solutions for polaron dynamics, including multi-polaron systems.

Findings

Derived the Schr"odinger-Poisson system from the Fr"ohlich model.

Analyzed the accuracy of the system in describing polaron motion.

Extended results to systems with multiple polarons.

Abstract

The polaron model of H. Fr\"ohlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit one expects that the phonon modes may be treated classically, which leads to a coupled Schr\"odinger-Poisson system with memory. For the effective dynamics of the electron this amounts to a nonlinear and non-local Schr\"odinger equation. We use the Dirac-Frenkel variational principle to derive the Schr\"odinger-Poisson system from the Fr\"ohlich model and we present new results on the accuracy of their solutions for describing the motion of Fr\"ohlich polarons in the strong-coupling limit. Our main result extends to $N$-polaron systems.