On the dynamics of polarons in the strong-coupling limit

Abstract

The polaron model of H. Fröhlich 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 Schrödinger–Poisson system with memory. For the effective dynamics of the electron, this amounts to a nonlinear and non-local Schrödinger equation. We use the Dirac–Frenkel variational principle to derive the Schrödinger–Poisson system from the Fröhlich model and we present new results on the accuracy of their solutions for describing the motion of Fröhlich polarons in the strong-coupling limit. Our main result extends to [Formula: see text]-polaron systems.