> preprints, articles, book chapters, proceedings, general audience articles, thesis, misc

Preprints

[5]
Mathieu Lewin. Semi-classical limit of the Levy-Lieb functional in Density Functional Theory. ArXiv e-prints, 2017. (arXiv:1706.02199)
[4]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits. ArXiv e-prints, 2017. (arXiv:1703.09422)
[3]
Mathieu Lewin, Phành Than Nam, and Nicolas Rougerie. Bose Gases at Positive Temperature and Non-Linear Gibbs Measures. In Proceedings of the International Congress of Mathematical Physics, 2015. ArXiv e-prints. (arXiv:1602.05166)
[2]
Mathieu Lewin. Mean-field limit of Bose systems: rigorous results. In Proceedings of the International Congress of Mathematical Physics, 2015. ArXiv e-prints. (arXiv:1510.04407)
[1]
Søren Fournais, Mathieu Lewin, and Jan Philip Solovej. The semi-classical limit of large fermionic systems. ArXiv e-prints, 2015. (arXiv:1510.01124)

Articles (published or accepted)

[63]
Mathieu Lewin. Existence of Hartree-Fock excited states for atoms and molecules. Lett. Math. Phys., online first, 2017. (arXiv:1708.00287) (doi:10.1007/s11005-017-1019-y)
[62]
Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer. Statistical Mechanics of the Uniform Electron Gas. J. Éc. polytech. Math., in press, 2017. (arXiv:1705.10676)
[61]
Maria J. Esteban, Mathieu Lewin, and Éric Séré. Domains for Dirac-Coulomb min-max levels. Rev. Mat. Iberoam., in press, 2017. (arXiv:1702.04976)
[60]
Philippe Gravejat, Mathieu Lewin, and Éric Séré. Derivation of the magnetic Euler-Heisenberg energy. J. Math. Pures Appl., in press, 2017. (arXiv:1602.04047) (doi:10.1016/j.matpur.2017.07.015)
[59]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. A note on 2D focusing many-boson systems. Proc. Amer. Math. Soc., 145(6):2441–2454, June 2017. (arXiv:1509.09045) (doi:10.1090/proc/13468)
[58]
Søren Fournais, Jonas Lampart, Mathieu Lewin, and Thomas Østergaard Sørensen. Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory. Phys. Rev. A, 93(6):062510, June 2016. (arXiv:1603.02219) (doi:10.1103/PhysRevA.93.062510)
[57]
Jonas Lampart and Mathieu Lewin. Semi-classical Dirac vacuum polarisation in a scalar field. Ann. Henri Poincaré, 17(8):1937–1954, 2016. (arXiv:1506.00895) (doi:10.1007/s00023-016-0472-y)
[56]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Trans. Amer. Math. Soc, 368(9):6131–6157, 2016. (arXiv:1405.3220) (doi:10.1090/tran/6537)
[55]
Xavier Blanc and Mathieu Lewin. The Crystallization Conjecture: A Review. EMS Surv. Math. Sci., 2(2):219–306, 2015. (arXiv:1504.01153) (doi:10.4171/EMSS/13)
[54]
Jonas Lampart and Mathieu Lewin. A many-body RAGE theorem. Comm. Math. Phys., 340(3):1171–1186, 2015. (arXiv:1503.00496) (doi:10.1007/s00220-015-2458-x)
[53]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. Derivation of nonlinear Gibbs measures from many-body quantum mechanics. J. Éc. polytech. Math., 2:65–115, 2015. (arXiv:1410.0335) (doi:10.5802/jep.18)
[52]
Mathieu Lewin and Elliott H. Lieb. Improved Lieb-Oxford exchange-correlation inequality with gradient correction. Phys. Rev. A, 91(2):022507, 2015. (arXiv:1408.3358) (doi:10.1103/PhysRevA.91.022507)
[51]
Mathieu Lewin and Simona Rota Nodari. Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation. NoDEA Nonlinear Differential Equations Appl., 22(4):673–698, 2015. (arXiv:1405.1165) (doi:10.1007/s00030-014-0300-3)
[50]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. Remarks on the quantum de Finetti theorem for bosonic systems. Appl. Math. Res. Express (AMRX), 2015(1):48–63, 2015. (arXiv:1310.2200) (doi:10.1093/amrx/abu006)
[49]
Mathieu Lewin and Julien Sabin. The Hartree equation for infinitely many particles. I. Well-posedness theory. Comm. Math. Phys., 334(1):117–170, 2015. (arXiv:1310.0603) (doi:10.1007/s00220-014-2098-6)
[48]
Mathieu Lewin, Phan Thành Nam, and Benjamin Schlein. Fluctuations around Hartree states in the mean-field regime. Amer. J. Math., 137(6):1613–1650, dec 2015. (arXiv:1307.0665) (doi:10.1353/ajm.2015.0040)
[47]
Mathieu Lewin, Phan Thành Nam, Sylvia Serfaty, and Jan Philip Solovej. Bogoliubov spectrum of interacting Bose gases. Comm. Pure Appl. Math., 68(3):413–471, march 2015. (arXiv:1211.2778) (doi:10.1002/cpa.21519)
[46]
Mathieu Lewin and Julien Sabin. The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D. Analysis & PDE, 7(6):1339–1363, 2014. (arXiv:1310.0604) (doi:10.2140/apde.2014.7.1339)
[45]
Mathieu Lewin and Julien Sabin. A family of monotone quantum relative entropies. Lett. Math. Phys., 104(6):691–705, 2014. (arXiv:1309.4046) (doi:10.1007/s11005-014-0689-y)
[44]
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer. Strichartz inequality for orthonormal functions. J. Eur. Math. Soc. (JEMS), 16:1507–1526, 2014. (arXiv:1306.1309) (doi:10.4171/JEMS/467)
[43]
Mathieu Lewin, Phan Thành Nam, and Nicolas Rougerie. Derivation of Hartree's theory for generic mean-field Bose systems. Adv. Math., 254:570–621, March 2014. (arXiv:1303.0981) (doi:10.1016/j.aim.2013.12.010)
[42]
Mathieu Lewin and Séverine Paul. A Numerical Perspective on Hartree-Fock-Bogoliubov Theory. ESAIM: M2AN, 48(1):53–86, 2014. (arXiv:1206.6081) (doi:10.1051/m2an/2013094)
[41]
Enno Lenzmann and Mathieu Lewin. Dynamical ionization bounds for atoms. Analysis & PDE, 6(5):1183–1211, 2013. (arXiv:1207.6898) (doi:10.2140/apde.2013.6.1183)
[40]
Philippe Gravejat, Christian Hainzl, Mathieu Lewin, and Éric Séré. Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields. Arch. Rat. Mech. Anal., 208(2):603–665, May 2013. (arXiv:1204.2893) (doi:10.1007/s00205-012-0609-1)
[39]
Éric Cancès, Salma Lahbabi, and Mathieu Lewin. Mean-field models for disordered crystals. J. Math. Pures Appl., 100(2):241–274, 2013. (arXiv:1203.0402) (doi:10.1016/j.matpur.2012.12.003)
[38]
Mathieu Lewin and Nicolas Rougerie. On the binding of polarons in a mean-field quantum crystal. ESAIM Control Optim. Calc. Var., 19(3):629–656, July 2013. (arXiv:1202.5103) (doi:10.1051/cocv/2012025)
[37]
Mathieu Lewin and Nicolas Rougerie. Derivation of Pekar's Polarons from a Microscopic Model of Quantum Crystals. SIAM J. Math. Anal., 45(3):1267–1301, 2013. (arXiv:1108.5931) (doi:10.1137/110846312)
[36]
Christian Hainzl, Mathieu Lewin, and Christof Sparber. Ground state properties of graphene in Hartree-Fock theory. J. Math. Phys., 53:095220, 2012. Special issue in honor of E.H. Lieb's 80th birthday. (arXiv:1203.5016) (doi:10.1063/1.4750049)
[35]
Xavier Blanc and Mathieu Lewin. Existence of the thermodynamic limit for disordered quantum Coulomb systems. J. Math. Phys., 53:095209, 2012. Special issue in honor of E.H. Lieb's 80th birthday. (arXiv:1201.4670) (doi:10.1063/1.4729052)
[34]
Mathieu Lewin. Comment on `Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry', by C. Argaez and M. Melgaard. Nonlinear Analysis: Theory, Methods & Applications, 75:2988–2991, 2012. (arXiv:1111.4491) (doi:10.1016/j.na.2011.12.001)
[33]
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer. A positive density analogue of the Lieb-Thirring inequality. Duke Math. J., 162(3):435–495, 2012. (arXiv:1108.4246) (doi:10.1215/00127094-2019477)
[32]
Lyonell Boulton, Nabile Boussaid, and Mathieu Lewin. Generalised Weyl theorems and spectral pollution in the Galerkin method. J. Spect. Theory, 2(4):329–354, 2012. (arXiv:1011.3634) (doi:10.4171/JST/32)
[31]
Enno Lenzmann and Mathieu Lewin. On singularity formation for the L2-critical Boson star equation. Nonlinearity, 24(12):3515, 2011. (arXiv:1103.3140) (doi:10.1088/0951-7715/24/12/009)
[30]
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer. Energy Cost to Make a Hole in the Fermi Sea. Phys. Rev. Lett., 106(15):150402, Apr 2011. (arXiv:1102.1414) (doi:10.1103/PhysRevLett.106.150402)
[29]
Mathieu Lewin. Geometric methods for nonlinear many-body quantum systems. J. Funct. Anal., 260:3535–3595, 2011. (arXiv:1009.2836) (doi:10.1016/j.jfa.2010.11.017)
[28]
Philippe Gravejat, Mathieu Lewin, and Éric Séré. Renormalization and asymptotic expansion of Dirac's polarized vacuum. Commun. Math. Phys., 306(1):1–33, 2011. (arXiv:1004.1734) (doi:10.1007/s00220-011-1271-4)
[27]
Maria J. Esteban, Mathieu Lewin, and Andreas Savin. Symmetry breaking of relativistic multiconfiguration methods in the nonrelativistic limit. Nonlinearity, 23:767–791, 2010. (arXiv:0910.3932) (doi:10.1088/0951-7715)
[26]
Christian Hainzl, Enno Lenzmann, Mathieu Lewin, and Benjamin Schlein. On blowup for time-dependent generalized Hartree-Fock equations. Ann. Henri Poincaré, 11(6):1023–1052, 2010. (arXiv:0909.3043) (doi:10.1007/s00023-010-0054-3)
[25]
Éric Cancès and Mathieu Lewin. The dielectric permittivity of crystals in the reduced Hartree-Fock approximation. Arch. Ration. Mech. Anal., 197(1):139–177, 2010. (arXiv:0903.1944) (doi:10.1007/s00205-009-0275-0)
[24]
Mathieu Lewin and Éric Séré. Spectral pollution and how to avoid it (with applications to Dirac and periodic Schrödinger operators). Proc. London Math. Soc., 100(3):864–900, 2010. (arXiv:0812.2153) (doi:10.1112/plms)
[23]
Enno Lenzmann and Mathieu Lewin. Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs. Duke Math. J., 152(2):257–315, 2010. (arXiv:0809.2560) (doi:10.1215/00127094-2010-013)
[22]
Christian Hainzl, Mathieu Lewin, and Éric Séré. Existence of atoms and molecules in the mean-field approximation of no-photon quantum electrodynamics. Arch. Ration. Mech. Anal., 192(3):453–499, 2009. (arXiv:math-ph/0606001) (doi:10.1007/s00205-008-0144-2)
[21]
Mathieu Lewin and Robert Seiringer. Strongly correlated phases in rapidly rotating Bose gases. J. Stat. Phys., 137(5-6):1040–1062, Dec 2009. (arXiv:0906.0741) (doi:10.1007/s10955-009-9833-y)
[20]
Christian Hainzl, Mathieu Lewin, and Jan Philip Solovej. The thermodynamic limit of quantum Coulomb systems. Part II. Applications. Advances in Math., 221:488–546, 2009. (arXiv:0806.1709) (doi:10.1016/j.aim.2008.12.011)
[19]
Christian Hainzl, Mathieu Lewin, and Jan Philip Solovej. The thermodynamic limit of quantum Coulomb systems. Part I. General theory. Advances in Math., 221:454–487, 2009. (arXiv:0806.1708) (doi:10.1016/j.aim.2008.12.010)
[18]
Marco Ghimenti and Mathieu Lewin. Properties of periodic Hartree-Fock minimizers. Calc. Var. Partial Differential Equations, 35(1):39–56, 2009. (arXiv:0803.3269) (doi:10.1007/s00526-008-0196-z)
[17]
Philippe Gravejat, Mathieu Lewin, and Éric Séré. Ground state and charge renormalization in a nonlinear model of relativistic atoms. Commun. Math. Phys., 286(1):179–215, 2009. (arXiv:0712.2911) (doi:10.1007/s00220-008-0660-9)
[16]
Jean Dolbeault, Patricio Felmer, and Mathieu Lewin. Stability of the Hartree-Fock model with temperature. Math. Models Methods Appl. Sci., 19(3):347–367, 2009. (doi:10.1142/S0218202509003450)
[15]
Éric Cancès, Amélie Deleurence, and Mathieu Lewin. A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case. Commun. Math. Phys., 281(1):129–177, 2008. (arXiv:math-ph/0702071) (doi:10.1007/s00220-008-0481-x)
[14]
Christian Hainzl, Mathieu Lewin, and Robert Seiringer. A nonlinear model for relativistic electrons at positive temperature. Rev. Math. Phys., 20(10):1283 –1307, 2008. (arXiv:0802.4054) (doi:10.1142/S0129055X08003547)
[13]
Maria J. Esteban, Mathieu Lewin, and Éric Séré. Variational methods in relativistic quantum mechanics. Bull. Amer. Math. Soc. (N.S.), 45(4):535–593, 2008. (arXiv:0706.3309) (doi:10.1090/S0273-0979-08-01212-3)
[12]
Éric Cancès, Amélie Deleurence, and Mathieu Lewin. Non-perturbative embedding of local defects in crystalline materials. J. Phys.: Condens. Matter, 20:294213, 2008. (arXiv:0706.0794) (doi:10.1088/0953-8984)
[11]
Christian Hainzl, Mathieu Lewin, and Jan Philip Solovej. The mean-field approximation in quantum electrodynamics: the no-photon case. Comm. Pure Appl. Math., 60(4):546–596, 2007. (arXiv:math-ph/0503075) (doi:10.1002/cpa.20145)
[10]
Christian Hainzl, Mathieu Lewin, Éric Séré, and Jan Philip Solovej. A minimization method for relativistic electrons in a mean-field approximation of quantum electrodynamics. Phys. Rev. A, 76:052104, 2007. (arXiv:0706.1486) (doi:10.1103/PhysRevA.76.052104)
[9]
Éric Cancès, Mathieu Lewin, and Gabriel Stoltz. The electronic ground-state energy problem: a new reduced density matrix approach. J. Chem. Phys., 125(6):64101, 2006. (arXiv:quant-ph/0602042) (doi:10.1063/1.2222358)
[8]
Mathieu Lewin. Solution of a mountain pass problem for the isomerization of a molecule with one free atom. Ann. Henri Poincaré, 7(2):365–379, 2006. (doi:10.1007/s00023-005-0252-6)
[7]
Éric Cancès, Hervé Galicher, and Mathieu Lewin. Computing electronic structures: a new multiconfiguration approach for excited states. J. Comput. Phys., 212(1):73–98, 2006. (doi:10.1016/j.jcp.2005.06.015)
[6]
Christian Hainzl, Mathieu Lewin, and Éric Séré. Self-consistent solution for the polarized vacuum in a no-photon QED model. J. Phys. A, 38(20):4483–4499, 2005. (arXiv:physics/0404047) (doi:10.1088/0305-4470)
[5]
Christian Hainzl, Mathieu Lewin, and Christof Sparber. Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation. Lett. Math. Phys., 72(2):99–113, 2005. (arXiv:math-ph/0412018) (doi:10.1007/s11005-005-4377-9)
[4]
Christian Hainzl, Mathieu Lewin, and Éric Séré. Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation. Commun. Math. Phys., 257(3):515–562, 2005. (arXiv:math-ph/0403005) (doi:10.1007/s00220-005-1343-4)
[3]
Mathieu Lewin. Solutions of the multiconfiguration equations in quantum chemistry. Arch. Ration. Mech. Anal., 171(1):83–114, 2004. (doi:10.1007/s00205-003-0281-6)
[2]
Mathieu Lewin. A mountain pass for reacting molecules. Ann. Henri Poincaré, 5(3):477–521, 2004. (doi:10.1007/s00023-004-0176-6)
[1]
Mathieu Lewin. The multiconfiguration methods in quantum chemistry: Palais-Smale condition and existence of minimizers. C. R. Math. Acad. Sci. Paris, 334(4):299–304, 2002. (doi:10.1016/S1631-073X(02)02252-5)

Book chapters

[1]
Mathieu Lewin and Éric Séré. Many-Electron Approaches in Physics, Chemistry and Mathematics, chapter Spurious Modes in Dirac Calculations and How to Avoid Them, pages 31–52. Mathematical Physics Studies. Springer International Publishing, 2014. (arXiv:1306.5401) (doi:10.1007/978-3-319-06379-9_2)

Proceedings

[14]
Philippe Gravejat, Christian Hainzl, Mathieu Lewin, and Éric Séré. Deux modèles effectifs pour les champs électromagnétiques dans le vide de Dirac. In Séminaire Laurent Schwartz – EDP et applications, page Exp. no. 14, 2015-2016.
[13]
Mathieu Lewin. A nonlinear variational problem in relativistic quantum mechanics. In R. Latala, A. Rucinski, P. Strzelecki, J. Swiatkowski, D. Wrzosek, and P. Zakrzewski, editors, Proceedings of the 6th European Congress of Mathematics, Krakow (Poland), July 2012. EMS, 2014. (arXiv:1209.2786)
[12]
Philippe Gravejat, Christian Hainzl, Mathieu Lewin, and Éric Séré. Two Hartree-Fock models for the vacuum polarization. In Proceedings of the ``Journées E.D.P.'', June 4–8, 2012, Biarritz (France), 2012. (arXiv:1209.6338)
[11]
Éric Cancès, Salma Lahbabi, and Mathieu Lewin. Mean-field electronic structure models for disordered materials. In Arne Jensen, editor, XVIIth International Congress on Mathematical Physics, pages 549–557. World Sci. Publ., 2012. (arXiv:1203.0402) (doi:10.1142/9789814449243_0057)
[10]
Mathieu Lewin. Gaz de bosons dans le régime de champ moyen : les théories de Hartree et Bogoliubov. In Séminaire Laurent Schwartz – EDP et applications. IHÉS, 2012-2013. Exp. no 3. (doi:10.5802/slsedp.33)
[9]
Éric Cancès, Mathieu Lewin, and Gabriel Stoltz. The microscopic origin of the macroscopic dielectric permittivity of crystals: A mathematical viewpoint. In Börn Engquist, Olof Runborg, and Yen-Hsi R. Tsai, editors, Numerical Analysis of Multiscale Computations, volume 82 of Lecture Notes in Computational Science and Engineering, pages 87–125. Springer, 2011. Proceedings of a Winter Workshop at the Banff International Research Station 2009. (arXiv:1010.3494) (doi:10.1007/978-3-642-21943-6)
[8]
Mathieu Lewin. Renormalization of Dirac's polarized vacuum. In Pavel Exner, editor, Mathematical Results In Quantum Physics, pages 45–59. World Scientific Publishing, 2011. Proceedings of the QMath 11 Conference, Hradec Kralove, Czech Republic, 6 –10 September 2010. (arXiv:1010.0075)
[7]
Mathieu Lewin. How much energy does it cost to make a hole in the fermi sea? Oberwolfach Reports, 8(2):1790–1793, 2011. Workshop ``Mathematical Methods in Quantum Chemistry''.
[6]
Mathieu Lewin. Sur l'effondrement dynamique des étoiles quantiques pseudo-relativistes. In Séminaire Laurent Schwartz. École Polytechnique, April 2011. (doi:10.5802/slsedp.10)
[5]
Christian Hainzl, Mathieu Lewin, and Jan Philip Solovej. The thermodynamic limit of quantum Coulomb systems: A new approach. In I. Beltita, G. Nenciu, and R. Purice, editors, Mathematical results in Quantum Mechanics: Proceedings of the QMath10 Conference. World Scientific, 2008. (arXiv:0806.2436) (doi:10.1142/9789812832382_0008)
[4]
Mathieu Lewin. On the computation of excited states with MCSCF methods. J. Math. Chem., 44(4):967–980, 2008. Conference ``Mathematical Methods for Ab Initio Quantum Chemistry'', Nice (FRANCE), Nov. 2005. (doi:10.1007/s10910-008-9355-x)
[3]
Mathieu Lewin. The thermodynamic limit of Quantum Coulomb Systems. Oberwolfach Reports, 4(1):399–400, 2007. Workshop ``Multiscale and Variational Methods in Material Science and Quantum Theory of Solids''.
[2]
Mathieu Lewin. On the computation of excited states with MCSCF methods. Oberwolfach Reports, 3(4):2833–2836, 2006. Workshop ``Mathematical and Numerical Aspects of Quantum Chemistry Problems''.
[1]
Mathieu Lewin. Solutions of the multiconfiguration equations in quantum chemistry. Oberwolfach Reports, 1(3):1541–1586, 2005. Workshop ``Calculus of variations'' June, 2004.

General audience articles

[3]
Mathieu Lewin. Bretzels, bagels, donuts et... topologie. CNRS Le Journal, 2017.
[2]
Mathieu Lewin. Limite de champ moyen et condensation de Bose-Einstein. Gazette des Mathématiciens, 139:35–49, Jan 2014. Société Mathématique de France.
[1]
Mathieu Lewin. Des cristaux et des maths. CNRS Le Journal, 2014.

Thesis

[2]
Mathieu Lewin. Large Quantum Systems: a Mathematical and Numerical Perspective. Habilitation à Diriger des Recherches, University of Cergy-Pontoise, June 2009.
[1]
Mathieu Lewin. Some nonlinear models in Quantum Mechanics. PhD thesis, University of Paris-Dauphine, June 2004.

Misc.

[2]
Mathieu Lewin. Éléments de théorie spectrale : le Laplacien sur un ouvert borné. Notes de cours de Master 2, 2017.
[1]
Mathieu Lewin. Post-Hartree-Fock Methods and Excited States Modeling. Encyclopedia of Applied and Computational Mathematics, Springer-Verlag, 2012.