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- Christian HAINZL, Mathieu Lewin, É. Séré
- 2005

According to Dirac’s ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator D. In the presence of an external field, these virtual particles react and the vacuum becomes polarized. In this paper, following Chaix and Iracane (J. Phys. B, 22, 3791–3814, 1989), we… (More)

- Philippe GRAVEJAT, Mathieu Lewin, É. Séré
- 2007

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a meanfield approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by… (More)

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb potential.

We present an overview of some works on the models of computational quantum chemistry. We examine issues such as the existence of ground states (both for the electronic structure and the configuration of nuclei), the foundations of the models of the crystalline phase, and the macroscopic limits. We emphasize the connections between the physical modelling,… (More)

- Philippe Gravejat, Mathieu Lewin, É. Séré, PHILIPPE GRAVEJAT
- 2010

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 and molecules while taking into account vacuum polarization effects. We consider the total physical density ρph including both the external density of a nucleus and the… (More)

- Christian HAINZL, Mathieu Lewin, É. Séré
- 2006

The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated minimizer, if it exists, will usually represent the ground state of a system of N electrons interacting with the Dirac… (More)

- Jean Dolbeault, Maria J. Esteban, É. Séré, M Vanbreugel
- Physical review letters
- 2000

Taking into account relativistic effects in quantum chemistry is crucial for accurate computations involving heavy atoms. Standard numerical methods can deal with the problem of variational collapse and the appearance of spurious roots only in special cases. The goal of this Letter is to provide a general and robust method to compute particle bound states… (More)

This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then, these results are applied to Dirac operators in… (More)

- B. Buffoni, É. Séré, J. F. Toland
- SIAM J. Math. Analysis
- 2005

Penalization and minimization methods are used to give an abstract “semiglobal” result on the existence of nontrivial solutions of parameter-dependent quasi-linear differential equations in variational form. A consequence is a proof of existence, by infinite-dimensional variational means, of bifurcation points for quasi-linear equations which have a line of… (More)

- Mathieu Lewin, Christian Hainzl, Philippe Gravejat, É. Séré
- 2010

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 polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off Λ. We then discuss the limit Λ → ∞… (More)