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Mathieu
PAGE PERSONNELLE DE MATHIEU LEWIN

puce Coordonnées (Retour)
Email : Mathieu.Lewin"@"math.cnrs.fr
Bureau : 5.09
Téléphone : (+33) 1 34 25 66 15
Fax : (+33) 1 34 25 66 45		 Département de Mathématiques
Université de Cergy-Pontoise / Saint-Martin
2, avenue Adolphe Chauvin
95 302 CERGY-PONTOISE Cedex
FRANCE

Principal Investigator of the ERC Starting Grant Mathematics and Numerics of Infinite Quantum Systems, managed by CNRS.


puce Thèmes de Recherche (Research Interests) (Retour)
- analyse non linéaire, équations aux dérivées partielles, théorie des points critiques ;
- physique mathématique, mécanique quantique relativiste et non relativiste, systèmes quantiques à grand nombre de particules, électrodynamique quantique ;
- calcul scientifique, simulation moléculaire.

english - nonlinear analysis, partial differential equations, critical point theory;
- mathematical physics, relativistic and non relativistic quantum mechanics, large quantum systems, quantum electrodynamics;
- numerical analysis, molecular simulations.


puce Publications (Retour) 
Refereed publications on MathSciNet

Pour télécharger les articles publiés originaux, cliquez ici   /   To download the original published papers, click here

triangle Research Articles

[43] - M.L., P.T. Nam & N. Rougerie. Derivation of Hartree's theory for generic mean-field Bose gases
Preprint arXiv. arXiv

[42] - M.L., P.T. Nam, S. Serfaty & J.P. Solovej. Bogoliubov Spectrum of Interacting Bose Gases
Comm. Pure Appl. Math., in press. arXiv

[41] - E. Lenzmann & M. L. Dynamical Ionization Bounds for Atoms
Analysis & PDE, in press. arXiv

[40] - M. L. & S. Paul. A Numerical Perspective on Hartree-Fock-Bogoliubov Theory
Preprint arXiv. arXiv

[39] - P. Gravejat, C. Hainzl, M. L. & E. Séré. Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
Arch. Rat. Mech. Anal. 208 (2013), no 2, 603-665. arXiv

[38] - C. Hainzl, M. L. & C. Sparber. Ground state properties of graphene in Hartree-Fock theory
J. Math. Phys. 53 (2012), 095220. Special issue in honor of E. H. Lieb's 80th birthday. arXiv

[37] - E. Cancès, S. Lahbabi & M. L. Mean-field models for disordered crystals
J. Math. Pure Appl., in press. arXiv

[36] - M. L. & N. Rougerie. On the binding of polarons in a mean-field quantum crystal
ESAIM Control Optim. Calc. Var., in press. arXiv

[35] - X. Blanc & M. L. Existence of the thermodynamic limit for disordered Coulomb quantum systems
J. Math. Phys. 53 (2012), 095209. Special issue in honor of E. H. Lieb's 80th birthday. arXiv

[34] - M. L. & N. Rougerie. Derivation of Pekar’s Polarons from a Microscopic Model of Quantum Crystals
SIAM J. Math. Anal., in press. arXiv

[33] - R. Frank, M. L., E.H. Lieb & R. Seiringer. A positive density analogue of the Lieb-Thirring inequality
Duke Math. Journal 162 (2012), no 3, 435-495. arXiv

[32] - L. Boulton, N. Boussaïd & M. L. Generalised Weyl theorems and spectral pollution in the Galerkin method.
J. Spectral Theory 2 (2012), no 4, 329-354. arXiv
 
[31] - E. Lenzmann & M. L. On singularity formation for the L^2-critical Boson star equation.
Nonlinearity 24 (2011), 3515. arXiv

[30] - R. Frank, M. L., E.H. Lieb & R. Seiringer. Energy Cost to Make a Hole in the Fermi Sea
Phys. Rev. Lett. 106 (2011), 150402. arXiv

[29] - M. L. Geometric methods for nonlinear many-body quantum systems.
J. Func. Anal. 260 (2011), 3535-3595.  arXiv

[28] - P. Gravejat, M. L. & E. Séré. Renormalization and asymptotic expansion of Dirac's polarized vacuum.
Comm. Math. Phys. 306 (2011), no. 1, 1-33. arXiv

[27] - C. Hainzl, E. Lenzmann, M. L. & B. Schlein. On blowup for time-dependent generalized Hartree-Fock equations.
Ann. Henri Poincaré 11 (2010), no 6, 1023-1052. arXiv

[26] - M. J. Esteban, M. L. & A. Savin. Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit.
Nonlinearity, 23 (2010), no. 4, 767-791. arXiv

[25] - E. Cancès & M. L. The dielectric permittivity of crystals in the reduced Hartree-Fock approximation.
Arch. Rational Mech. Anal, 197 (2010), no 1, 139-177. arXiv

[24] - E. Séré & M.L. Spectral pollution and how to avoid it (with applications to Dirac and periodic Schrödinger operators).
Proc. London Math. Soc., 100 (2010), no 3, 864-900. arXiv
 
[23] - E. Lenzmann & M.L. Minimizers for the Hartree-Fock-Bogoliubov Theory of Neutron Stars and White dwarfs.
Duke Math. Journal ,152 (2010), no. 2, 257-315. arXiv

 [22] - M. L. & R. Seiringer. Strongly correlated phases in rapidly rotating Bose gases.
J. Stat. Phys, 137 (2009), no. 5-6, 1040-1062. arXiv
 
[21] - C. Hainzl, M. L. & J.P. Solovej. The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications.
Advances in Math. 221 (2009), 488-546. arXiv
 
[20] - C. Hainzl, M. L. & J.P. Solovej. The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory.
Advances in Math. 221 (2009), 454-487. arXiv
 
[19] - J. Dolbeault, P. Felmer & M. L. Stability of the Hartree-Fock model with temperature.
Math. Model Meth. Appl. Sci. 19 (2009), no.3, 347-367. arXiv
 
[18] - P. Gravejat, M. L. & E. Séré. Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms.
Commun. Math. Phys. 286 (2009), no. 1, 179-215. arXiv
 
[17] - M. Ghimenti & M. L. Properties of periodic Hartree-Fock minimizers.
Calc. Var. Partial Differential Equations, 35 (2009), no. 1, 39-56. arXiv

[16] - C. Hainzl, M. L. & E. Séré. Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics.
Arch. Rational Mech. Anal, 192 (2009), no. 3, 453-499. arXiv
 
[15] - C. Hainzl, M. L. & R. Seiringer. A Nonlinear Model for Relativistic Electrons At Positive Temperature.
Rev. Math. Phys. 20 (2008), no. 10, 1283-1307. arXiv

[14] - E. Cancès, A. Deleurence & M. L. Non-perturbative embedding of local defects in crystalline materials.
J. Phys.: Condens. Matter. 20 (2008), 294213. arXiv
 
[13] - E. Cancès, A. Deleurence & M. L. A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case.
Commun. Math. Phys. 281 (2008), 129–177.  arXiv
 
[12] - M. J. Esteban, M. L. & E. Séré. Variational methods in relativistic quantum mechanics.
Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 4, 535–593. arXiv
 
[11] - C. Hainzl, M. L., E. Séré & J.P. Solovej. A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics.
Phys. Rev. A 76 (2007), 052104. arXiv
 
[10] - C. Hainzl, M. L. & J.P. Solovej. The mean-field approximation in Quantum Electrodynamics. The no-photon case.
Comm. Pure Appl. Math. 60 (2007), no. 4, 546-596. arXiv
 
[9] - E. Cancès, M.L. & G. Stoltz. The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach.
J. Chem. Phys. 125 (2006), 064101-064106.  arXiv
 
[8] - M. L. Solution of a mountain pass problem for the isomerization of a molecule with one free atom.
Ann. Henri Poincaré 7 (2006), 365-379. PDF
 
[7] - E. Cancès, H. Galicher & M. L. Computing electronic structures : a new multiconfiguration approach for excited states.
J. Comput. Phys. 212 (2006), 73-98. PDF
 
[6] - C. Hainzl, M. L. & C. Sparber. Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation.
Lett. Math. Phys. 72 (2005), no 2, 99-113. arXiv
 
[5] - C. Hainzl, M. L. & E. Séré. Self-consistent solution for the polarized vacuum in a no-photon QED model.
J. Phys. A: Math & Gen. 38 (2005), no 20, 4483-4499. arXiv
 
[4] - C. Hainzl, M. L. & E. Séré. Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation.
Commun. Math. Phys. 257 (2005), 515-562 . arXiv
 
[3] - M. L. A Mountain Pass for Reacting Molecules.
Ann. Henri Poincaré 5 (2004), no 3, 477-521. PDF
 
[2] - M. L. Solutions of the Multiconfiguration Equations in Quantum Chemistry.
Arch. Rational Mech. Anal. 171 (2004), no 1, 83-114. PDF
 
[1] - M. L. The multiconfiguration methods in quantum chemistry: Palais-Smale condition and existence of minimizers.
C. R. Acad. Sci. Paris, Ser. I 334 (2002), no 4, 299--304. PDF

triangle Proceedings
 
[l] - M.L. Gaz de bosons dans le régime de champ moyen : les théories de Hartree et Bogoliubov
Séminaire X-EDP, IHES, 20 Novembre 2013. hal
 
[k] - P. Gravejat, C. Hainzl, M. L. & E. Séré. Two Hartree-Fock models for the vacuum polarization
Proceeding of the Journées E.D.P., Biarritz (France), June 4-8, 2012. arXiv
 
[j] - E. Cancès, S. Lahbabi & M. L. Mean-field electronic structure models for disordered materials
Proceeding of the International Congress on Mathematical Physics, Aalborg (Denmark), August 2012.
 
[i] - M.L. A nonlinear variational problem in relativistic quantum mechanics arXiv
Proceeding of the 6th European Congress of Mathematics, Krakow (Poland), July 2012.
 
[h] - M.L. Sur l'effondrement dynamique des étoiles quantiques pseudo-relativistes
Séminaire X-EDP, Ecole Polytechnique, 5 Avril 2011. PDF
 
[g] - M.L. Renormalization of Dirac's Polarized Vacuum.
Proceedings of the Conference QMath 11 held in Hradec Kralové (Czechia) in September 2010. arXiv
 
[f] - E. Cancès, M.L. & G. Stoltz. The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint.
Proceedings of the Workshop "Numerical Analysis of Multiscale Computations" at Banff International Research Station, December 2009. arXiv
 
[e] - C. Hainzl, M.L. & J.P. Solovej. The Thermodynamic Limit of Quantum Coulomb Systems: A New Approach.
Mathematical results in Quantum Mechanics: Proceedings of the QMath10 Conference, World Scientific, Eds: I. Beltita, G. Nenciu & R. Purice, 2008. arXiv
 
[d] - M.L. The Thermodynamic Limit of Quantum Coulomb Systems.
Workshop ``Multiscale and Variational Methods in Material Science and Quantum Theory of Solids".
Oberwolfach Reports, 4 (2007), no. 1, 399-400.
 
[c] - M.L. On the Computation of Excited States with MCSCF Methods.
Workshop ``Mathematical and Numerical Aspects of Quantum Chemistry Problems".
Oberwolfach Reports, 3 (2006), no. 4, 2833-2836.
 
[b] - M.L. On the Computation of Excited States with MCSCF Methods.
Conference "Mathematical Methods for Ab Initio Quantum Chemistry", Nice (FRANCE), Nov. 2005.
J. Math. Chem., 44 (2008), no. 4, 967-980. PDF
 
[a] - M. L. Solutions of the Multiconfiguration Equations in Quantum Chemistry.
Workshop ``Calculus of variations" June, 2004.
Oberwolfach Reports, 1 (2005), no. 3, 1541-1586.

triangle Other
M. L. Quelques modèles non linéaires en mécanique quantique
(Some nonlinear models in quantum mechanics)
PhD Thesis, Université Paris Dauphine, 21 Juin 2004.
 
M. L. Systèmes quantiques à grand nombre de particules : une perspective mathématique et numérique
(Large quantum systems: a mathematical and numerical perspective)
Habilitation à Diriger des Recherches, Université de Cergy-Pontoise, 9 Juin 2009. PDF


puce Projects / Collaborations (Retour)
triangle Principal Investigator of the ERC Starting Grant Mathematics and Numerics of Infinite Quantum Systems, managed by CNRS
triangle Coordinator of the ANR Project NoNAP (ANR-10-BLAN 0101).
triangle External collaborator of the project Simulation Moléculaire et Multi-échelles (Molecular and Multiscale Modelling) - CERMICS / INRIA.
triangle Former member of the project MathAmSud "Nonlinear Analysis and Partial Differential Equations".
triangle Former member of the project ANR ACCQUAREL (Approches Computationnelles en Chimie QUAntique RELativiste).
triangle Former member of the european network Analysis and Quantum.
triangle Former member of the program ECOS/CONYCIT (Chile) Partial Differential Equations of Mathematical Physics 


puce Enseignement (Retour)
triangle 2009/2010: Cours de l'école doctorale, Université de Cergy-Pontoise.
triangle 2007/2012: Cours avec Eric Cancès au M2 "Mathématiques de la modélisation", Université Pierre et Marie Curie. Page web du cours 
triangle 2006/2012 : Cours / TD avec Frédéric Legoll à l'ENPC "Mathématiques des modèles multi-échelles". Page web du cours
triangle Sept 2002 - Août 2004 : moniteur à l'UFR MD, Université Paris Dauphine.


puce Autres (Retour)
triangle Thematic Trimester "Spectral and Variational Methods in Quantum Mechanics", Institut Henri Poincaré, Spring 2013
triangle Conference "Mathematical Aspects of Quantum Electrodynamics" - Paris June 21-25, 2010


puce Quelques Liens (Retour)
Le site du département de Mathématiques
Le CEREMADE
Le Laboratoire Jacques-Louis Lions
Le CERMICS
Le Département de Maths de l'université de Copenhague
Le Projet MICMAC de l'INRIA
Le Projet ANR ACCQUAREL
Le Réseau Européen "Analysis and Quantum"
Le CNRS