Gabriel Stoltz École Nationale des Ponts-et-Chaussées (ENPC) CERMICS We study the response of crystals to external, static or time-dependent forcings by considering the properties of localized defects and their time evolutions. The aim of our work is to provide a mathematical analysis of the Adler-Wiser formula relating the (possibly frequency dependent) macroscopic relative permittivity tensor to the microscopic structure of the crystal at the atomic level.