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 $N$-polaron systems.

21 pages