117 citations · 1.9k across the 89 of their papers we have counts for
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Generalised Weyl theorems and spectral pollution in the Galerkin method
Lyonell Boulton, Nabile Boussaid, Mathieu Lewin
We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl seque…
The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint
Eric Cancès, Mathieu Lewin, Gabriel Stoltz
The purpose of this paper is to provide a mathematical analysis of the Adler-Wiser formula relating the macroscopic relative permittivity tensor to the microscopic structure of the…
Renormalization of Dirac's Polarized Vacuum
Mathieu Lewin
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the pola…
Geometric methods for nonlinear many-body quantum systems
Mathieu Lewin
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schrödinger operators. In this paper we provide a formalism which al…
Renormalization and asymptotic expansion of Dirac's polarized vacuum
Philippe Gravejat, Mathieu Lewin, Eric Séré
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms an…