Derivation of pekar's polarons from a microscopic model of quantum crystal

A polaron is an electron interacting with a polar crystal, which is able to form a bound state by using the distortions of the crystal induced by its own density of charge. In this paper we consider the case of a very light charged particle which is inserted in a quantum crystal described by reduced Hartree-Fock theory. Due to its small mass, the polaron lives on a much larger scale than the characteristic length of the host crystal. In the limit of very small mass, the macroscopic density of the polaron converges to that of Pekar's nonlinear model, with a possibly anisotropic dielectric matrix. The polaron also exhibits fast microscopic oscillations which contribute to the energy at the same order but whose characteristic length is small compared to the scale of the polaron. These oscillations are described by a simple periodic eigenvalue equation. Our approach also covers multipolarons composed of several particles, repelling each other via Coulomb forces.