Teta: Towards a rigorous derivation of the cubic NLSE in dimension one, Asymptot. Anal, vol.40, issue.2, pp.93-108, 2004. ,
Rigorous Derivation of the Cubic NLS in Dimension One, Journal of Statistical Physics, vol.127, issue.6, pp.1193-1220, 2007. ,
DOI : 10.1007/s10955-006-9271-z
Complex analysis. An introduction to the theory of analytic functions of one complex variable, Third edition. International Series in Pure and Applied Mathematics, 1978. ,
Setting and Analysis of the Multi-configuration Time-dependent Hartree???Fock Equations, Archive for Rational Mechanics and Analysis, vol.37, issue.8, pp.273-330, 2010. ,
DOI : 10.1007/s00205-010-0308-8
URL : https://hal.archives-ouvertes.fr/hal-00370704
Mauser: The TDHF approximation for Hamiltonians with m-particle interaction potentials, Commun . Math. Sci, pp.1-9, 2007. ,
Derivation of the Schr??dinger???Poisson equation from the quantum -body problem, Comptes Rendus Mathematique, vol.334, issue.6, pp.515-520, 2002. ,
DOI : 10.1016/S1631-073X(02)02253-7
Weak coupling limit of the N particles Schrödinger equation, Methods Appl. Anal, vol.7, issue.2, pp.275-293, 2000. ,
Mean field dynamics of fermions and??the??time-dependent??Hartree???Fock equation, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.6, pp.665-683, 2003. ,
DOI : 10.1016/S0021-7824(03)00023-0
Accuracy of the Time-Dependent Hartree???Fock Approximation for Uncorrelated Initial States, Journal of Statistical Physics, vol.115, issue.3/4, pp.1037-1055, 2004. ,
DOI : 10.1023/B:JOSS.0000022381.86923.0a
URL : https://hal.archives-ouvertes.fr/hal-00021079
Mauser: On the derivation of nonlinear Schrödinger and Vlasov equations, in " Dispersive transport equations and multiscale models Mauser: One particle equations for many particle quantum systems: the MCTHDF method, Math. Appl. Quart. Appl. Math, vol.136, issue.1, pp.1-23, 2000. ,
Quantum Mechanics, 2005. ,
N-particle approximation to the nonlinear Vlasov???Poisson system, Nonlinear Analysis: Theory, Methods & Applications, vol.47, issue.3, pp.1445-1456, 2000. ,
DOI : 10.1016/S0362-546X(01)00280-2
Convergence of Probability Measures, 1999. ,
DOI : 10.1002/9780470316962
Classical Solutions and the Glassey-Strauss Theorem for the 3D Vlasov-Maxwell System, Archive for Rational Mechanics and Analysis, vol.170, issue.1, pp.1-15, 2003. ,
DOI : 10.1007/s00205-003-0265-6
Pallard: Nonresonant smoothing for coupled wave + transport equations; applications to the Vlasov-Maxwell system, Rev. Mat. Iberoamericana, vol.20, pp.865-892, 2004. ,
Kinetic Equations and Asymptotic Theory, L. Desvillettes et B. Perthame eds, Series in Applied Mathematics , 4. Gauthier-Villars, Editions Scientifiques et Médicales Elsevier, 2000. ,
An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction, Communications in Mathematical Physics, vol.6, issue.3, pp.183-191, 1974. ,
DOI : 10.1007/BF01646344
On the Hartree-Fock time-dependent problem, Communications in Mathematical Physics, vol.78, issue.1, pp.25-33, 1976. ,
DOI : 10.1007/BF01608633
Hepp: The Vlasov Dynamics and Its Fluctuations in the 1/N Limit of Interacting Classical Particles, Commun. Math. Phys, pp.56-101, 1977. ,
Probability, 1968. ,
DOI : 10.1137/1.9781611971286
Analyse fonctionnelle. Théorie et applications, 1987. ,
A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Communications in Mathematical Physics, vol.187, issue.3, pp.501-525, 1992. ,
DOI : 10.1007/BF02099262
ON THE TIME-DEPENDENT HARTREE???FOCK EQUATIONS COUPLED WITH A CLASSICAL NUCLEAR DYNAMICS, Mathematical Models and Methods in Applied Sciences, vol.09, issue.07, pp.963-990, 1999. ,
DOI : 10.1142/S0218202599000440
On the Boltzmann equation for rigid spheres, Transport Theory Statist, Phys, vol.2, issue.3, pp.211-225, 1972. ,
The mathematical theory of dilute gases, Applied Mathematical Sciences, vol.106, 1994. ,
DOI : 10.1007/978-1-4419-8524-8
Global existence of solutions to the Cauchy problem for time???dependent Hartree equations, Journal of Mathematical Physics, vol.16, issue.5, pp.1122-1130, 1975. ,
DOI : 10.1063/1.522642
On particle-in-cell methods for the Vlasov-Poisson equations, Transport Theory and Statistical Physics, vol.29, issue.1-2, pp.1-31, 1986. ,
DOI : 10.1137/0721003
Vlasov equations, Functional Analysis and Its Applications, vol.5, issue.3, pp.115-123, 1979. ,
DOI : 10.1007/BF01077243
Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons, Archive for Rational Mechanics and Analysis, vol.179, issue.2, pp.265-283, 2006. ,
DOI : 10.1007/s00205-005-0388-z
The Vlasov Limit for a System of Particles which Interact with a Wave Field, Communications in Mathematical Physics, vol.30, issue.2, pp.673-712, 2009. ,
DOI : 10.1007/s00220-008-0591-5
Derivation of the nonlinear Schr??dinger equation from a many-body Coulomb system, Advances in Theoretical and Mathematical Physics, vol.5, issue.6, pp.1169-1205, 2001. ,
DOI : 10.4310/ATMP.2001.v5.n6.a6
Derivation of the cubic non-linear Schr??dinger equation from quantum dynamics of many-body systems, Inventiones mathematicae, vol.116, issue.4, pp.515-614, 2007. ,
DOI : 10.1007/s00222-006-0022-1
Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate, Annals of Mathematics, vol.172, issue.1, pp.172-291, 2010. ,
DOI : 10.4007/annals.2010.172.291
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction, Communications in Mathematical Physics, vol.56, issue.17, pp.1023-1059, 2009. ,
DOI : 10.1007/s00220-009-0754-z
A Microscopic Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Two-Body Interaction, Journal of Statistical Physics, vol.56, issue.4, pp.23-50, 2011. ,
DOI : 10.1007/s10955-011-0311-y
Texier: From Newton to Boltzmann: the case of hard sphere potentials, preprint arXiv, pp.1208-5753 ,
Equations de champ moyen pour la dynamique quantique d'un grand nombre de particules (d'après Bardos, Exp. no. 930, pp.147-164, 2003. ,
On a class of non linear Schr???dinger equations with non local interaction, Mathematische Zeitschrift, vol.16, issue.2, pp.109-145, 1980. ,
DOI : 10.1007/BF01214768
The classical field limit of scattering theory for non-relativistic many-boson systems. I, Communications In Mathematical Physics, vol.14, issue.1, pp.37-76, 1979. ,
DOI : 10.1007/BF01197745
The Cauchy problem in kinetic theory, Society for Industrial and Applied Mathematics (SIAM), 1996. ,
DOI : 10.1137/1.9781611971477
The Mean-Field Limit for the Dynamics of Large Particle Systems, Journées Equations aux Dérivées Partielles, 2003. ,
The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics, Communications in Mathematical Physics, vol.8, issue.3, pp.310-789, 2012. ,
DOI : 10.1007/s00220-011-1377-8
URL : https://hal.archives-ouvertes.fr/hal-00545569
Empirical measures and mean field hierarchies ,
Convergence of the point vortex method for the 2-D euler equations, Communications on Pure and Applied Mathematics, vol.25, issue.3, pp.415-430, 1990. ,
DOI : 10.1002/cpa.3160430305
New stability estimates for the 2-D vortex method, Communications on Pure and Applied Mathematics, vol.24, issue.8-9, pp.1015-1031, 1991. ,
DOI : 10.1002/cpa.3160440813
Propagation of chaos for the Boltzmann equation, Archive for Rat, Mech. Anal, vol.42, pp.323-345, 1971. ,
WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.19, issue.08, pp.1357-1384, 2009. ,
DOI : 10.1142/S0218202509003814
N-particles Approximation of the Vlasov Equations with Singular Potential, Archive for Rational Mechanics and Analysis, vol.176, issue.3, pp.489-524, 2007. ,
DOI : 10.1007/s00205-006-0021-9
URL : https://hal.archives-ouvertes.fr/hal-00000670
Jabin: Propagation of chaos for particles approximations of Vlasov equations with singular forces ,
The classical limit for quantum mechanical correlation functions, Communications in Mathematical Physics, vol.67, issue.4, pp.265-277, 1974. ,
DOI : 10.1007/BF01646348
Symmetric measures on Cartesian products, Transactions of the American Mathematical Society, vol.80, issue.2, pp.470-501, 1955. ,
DOI : 10.1090/S0002-9947-1955-0076206-8
The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis, Classics in Mathematics, 2003. ,
The analysis of linear partial differential operators. III. Pseudo-differential operators, Classics in Mathematics, 2007. ,
The analysis of linear partial differential operators. IV. Fourier integral operators, Classics in Mathematics, 2009. ,
Lectures on nonlinear hyperbolic differential equations, Mathmatiques & Applications, vol.26, 1997. ,
Mean rates of convergence of empirical measures in the Wasserstein metric, Journal of Computational and Applied Mathematics, vol.55, issue.3, pp.261-273, 1994. ,
DOI : 10.1016/0377-0427(94)90033-7
Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, pp.171-197, 1954. ,
Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc, vol.70, pp.195-211, 1951. ,
Perturbation theory for linear operators, Classics in Mathematics, 1995. ,
Statistical mechanics of classical particles with logarithmic interactions, Communications on Pure and Applied Mathematics, vol.6, issue.1, pp.27-56, 1993. ,
DOI : 10.1002/cpa.3160460103
On the Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy, Communications in Mathematical Physics, vol.120, issue.5, pp.169-185, 2008. ,
DOI : 10.1007/s00220-008-0426-4
Mean-Field Dynamics: Singular Potentials and Rate of Convergence, Communications in Mathematical Physics, vol.53, issue.3, pp.101-138, 2010. ,
DOI : 10.1007/s00220-010-1010-2
Quantum mechanics: non-relativistic theory Translated from the Russian by, Course of Theoretical Physics, 1958. ,
Time evolution of large classical systems, Battelle Res. Inst. Lecture Notes in Phys, vol.38, pp.1-111, 1974. ,
DOI : 10.1007/3-540-07171-7_1
The Hartree-Fock theory for Coulomb systems, Communications in Mathematical Physics, vol.22, issue.3, pp.185-194, 1977. ,
DOI : 10.1007/BF01609845
Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Inventiones Mathematicae, vol.33, issue.no 1, pp.415-430, 1991. ,
DOI : 10.1007/BF01232273
Integration and Probability, Graduate Texts in Math, vol.157, 1995. ,
DOI : 10.1007/978-1-4612-4202-4
Mathematical Theory of Incompressible Nonviscous Fluids, 1994. ,
DOI : 10.1007/978-1-4612-4284-0
Kacs program in kinetic theory, Invent. Math., published online, pp.10-1007 ,
Wennberg: A new approach to quantitative propagation of chaos for drift, diffusion and jump processes, preprint arXiv 1101, p.4727 ,
Vlasov hydrodynamics of a quantum mechanical model, Communications in Mathematical Physics, vol.71, issue.1, pp.9-24, 1981. ,
DOI : 10.1007/BF01208282
Die Approximation der L??sung von Integro-Differentialgleichungen durch endliche Punktmengen, Lecture Notes in Math, vol.395, pp.275-290, 1974. ,
DOI : 10.1007/BFb0060678
An abstract form of the nonlinear Cauchy-Kowalewski theorem, Journal of Differential Geometry, vol.6, issue.4, pp.561-576, 1972. ,
DOI : 10.4310/jdg/1214430643
A note on a theorem of Nirenberg, Journal of Differential Geometry, vol.12, issue.4, pp.629-633, 1977. ,
DOI : 10.4310/jdg/1214434231
A nonlinear Cauchy problem in a scale of Banach spaces. (Russian) Dokl. Akad, Nauk SSSR, vol.200, pp.789-792, 1971. ,
Global classical soutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq, pp.95-281, 1992. ,
Mass transportation problems. Vol. I. Theory, Probability and its Applications, 1998. ,
Global Weak Solutions to the Relativistic Vlasov-Maxwell System Revisited, Communications in Mathematical Sciences, vol.2, issue.2, pp.145-158, 2004. ,
DOI : 10.4310/CMS.2004.v2.n2.a1
Collisionless kinetic equations from astrophysicsthe Vlasov- Poisson system, Handbook of differential equations: evolutionary equations, Handb. Differ. Equ, vol.III, pp.383-476, 2007. ,
Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics, Communications in Mathematical Physics, vol.52, issue.3, pp.31-61, 2009. ,
DOI : 10.1007/s00220-009-0867-4
The point-vortex method for periodic weak solutions of the 2-D Euler equations, Communications on Pure and Applied Mathematics, vol.49, issue.9, pp.911-965, 1996. ,
DOI : 10.1002/(SICI)1097-0312(199609)49:9<911::AID-CPA2>3.0.CO;2-A
Geometric wave equations, Courant Lecture Notes in Mathematics, vol.2, 1998. ,
DOI : 10.1090/cln/002
Kinetic equations from hamiltonian dynamics, Rev. Mod. Phys, vol.52, issue.3, pp.600-640, 1980. ,
DOI : 10.1103/revmodphys.52.569
On the Vlasov hierarchy, Mathematical Methods in the Applied Sciences, vol.56, issue.1, p.445455, 1981. ,
DOI : 10.1002/mma.1670030131
Large scale dynamics of interacting particles ,
DOI : 10.1007/978-3-642-84371-6
Topics in propagation of chaos, Ecole d'´ eté de Probabilités de Saint-Flour XIX?1989, Lecture Notes in Math, pp.165-251, 1464. ,
The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem, Japan Journal of Industrial and Applied Mathematics, vol.12, issue.2, pp.383-392, 2001. ,
DOI : 10.1007/BF03168581
Okabe: On classical solutions in the large in time of two dimensional Vlasov's equation, Osaka J. Math, vol.15, pp.245-261, 1978. ,
Topics in Optimal Transportation, American Math. Soc. Providence RI, vol.58, 2003. ,
DOI : 10.1090/gsm/058
Optimal Transport: Old and New, 2009. ,
DOI : 10.1007/978-3-540-71050-9
On the Approximation of the Vlasov--Poisson System by Particle Methods, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1369-1398, 2000. ,
DOI : 10.1137/S0036142999298528