2016/12/01 by Marcel Griesemer · 25 citations
Mathematics · Physics and Astronomy · #Dynamics (music) #Limit (mathematics) #Mechanical and Optical Resonators #Motion (physics) #Nonlinear Photonic Systems #Nonlinear system #Phonon #Polaron #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #msc:35Q55 #msc:81V99
paper · pdf · doi:10.1142/s0129055x17500301
published in Reviews in Mathematical Physics 29(10), 1750030 (World Scientific) · 21 pages
arxiv created 2016/12/01 · openalex created_date 2016/12/16 · openalex publication_date 2017/09/05 · arxiv updated 2017/11/22 · openalex updated_date 2026/08/05
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.