688 citations
- Centre de Recherche en Mathématiques de la DécisionFR60 papers
- Centre National de la Recherche ScientifiqueFR35 papers
- Centre de Recherche en Économie et StatistiqueFR11 papers
- Université Paris CitéFR11 papers
- École PolytechniqueFR6 papers
- Georgia Institute of TechnologyUS6 papers
- Sorbonne UniversitéFR5 papers
- Institut national de recherche en sciences et technologies du numériqueFR4 papers
- Laboratoire Traitement et Communication de l’InformationFR4 papers
- Analyse, Géométrie et ModélisationFR3 papers
- Center for Mathematical ModelingCL3 papers
- Centre for Research in Engineering Surface TechnologyIE3 papers
7 papers · 1 filter
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…
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
Philippe Gravejat, Mathieu Lewin, Eric Sere
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…
Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance
José Alfredo Cañizo
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discret…
Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
Jean Dolbeault, Patricio Felmer, Michael Loss +1
We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. Thi…
Binding energy for hydrogen-like atoms in the Nelson model without cutoffs
Christian Hainzl, Masao Hirokawa, Herbert Spohn
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge , , fixed at the origin an…
An analytical proof of Hardy-like inequalities related to the Dirac operator
J. Dolbeault, M. J. Esteban, M. Loss +1
We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral inf…