The mean-field limit for the dynamics of large particle systems
Journées équations aux dérivées partielles (2003)
- page 1-47
- ISSN: 0752-0360
Access Full Article
topAbstract
topHow to cite
topGolse, François. "The mean-field limit for the dynamics of large particle systems." Journées équations aux dérivées partielles (2003): 1-47. <http://eudml.org/doc/93451>.
@article{Golse2003,
abstract = {This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.},
author = {Golse, François},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-47},
publisher = {Université de Nantes},
title = {The mean-field limit for the dynamics of large particle systems},
url = {http://eudml.org/doc/93451},
year = {2003},
}
TY - JOUR
AU - Golse, François
TI - The mean-field limit for the dynamics of large particle systems
JO - Journées équations aux dérivées partielles
PY - 2003
PB - Université de Nantes
SP - 1
EP - 47
AB - This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.
LA - eng
UR - http://eudml.org/doc/93451
ER -
References
top- [25] R. Adami, C. Bardos, F. Golse, A. Teta, Towards a rigorous derivation of the cubic nonlinear Schrödinger equation in dimension 1, preprint. Zbl1069.35082
- [26] C. Bardos, L. Erdös, F. Golse, N. Mauser,H.-T. Yau, Derivation of the Schrödinger-Poisson equation from the quantum N-body problem, C. R. Acad. Sci. Sér. I Math 334 (2002), 515-520. Zbl1018.81009MR1890644
- [27] C. Bardos, F. Golse, A. Gottlieb, N. Mauser, Mean field dynamics of fermions and the time-dependent Hartree-Fock equation, to appear in J. de Math. Pures et Appl. 82 (2003). Zbl1029.82022MR1996777
- [28] C. Bardos, F. Golse, A. Gottlieb, N. Mauser, Derivation of the Time-Dependent Hartree-Fock Equation with Coulomb Potential, in preparation. Zbl1029.82022
- [30] C. Bardos, F. Golse, N. Mauser, Weak coupling limit of the N-particle Schrödinger equation, Methods Appl. Anal. 7 (2000), no. 2, 275-293. Zbl1003.81027MR1869286
- [31] A. Bove, G. DaPrato, G. Fano, An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction, Commun. Math. Phys. 37 (1974), 183-191. Zbl0303.34046MR424069
- [32] A. Bove, G. DaPrato, G. Fano, On the Hartree-Fock time-dependent problem, Comm. Math. Phys. 49 (1976), 25-33. MR456066
- [33] W. Braun, K. Hepp, The Vlasov Dynamics and Its Fluctuations in the 1/N Limit of Interacting Classical Particles; Commun. Math. Phys. 56 (1977), 101-113. Zbl1155.81383MR475547
- [34] E. Caglioti, P.-L. Lions, C. Marchioro, M. Pulvirenti: A special class of flows for two-dimensional Euler equations: a statistical mechanics description, Commun. Math. Phys. 143 (1992), 501-525. Zbl0745.76001MR1145596
- [35] E. Cancès, C. Le Bris, On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics, Math. Models Methods Appl. Sci. 9 (1999), 963-990. Zbl1011.81087MR1710271
- [36] I. Catto, C. Le Bris, P.-L. Lions, The mathematical theory of thermodynamic limits: Thomas-Fermi type models, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, (1998). Zbl0938.81001MR1673212
- [37] J.M. Chadam, R.T. Glassey, Global existence of solutions to the Cauchy problem for time-dependent Hartree equations, J. Mathematical Phys. 16 (1975), 1122-1130. Zbl0299.35084MR413843
- [38] L. Desvillettes, C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation; preprint. Zbl1162.82316MR1787105
- [39] R. Dobrushin, Vlasov equations; Funct. Anal. Appl. 13 (1979), 115-123. Zbl0422.35068MR541637
- [40] L. Erdös, H.-T. Yau: Derivation of the nonlinear Schrödinger equation from a many body Coulomb system, Adv. Theor. Math. Phys. 5 (2001), 1169-1205. Zbl1014.81063MR1926667
- [41] G. Gallavotti, Rigorous theory of the Boltzmann equation in the Lorentz gas, Nota int. no. 358, Istituto di Fisica, Università di Roma, (1972). Reprinted in Statistical Mechanics: a Short Treatise, pp. 48-55, Springer-Verlag Berlin-Heidelberg (1999)
- [42] M. Kiessling, Statistical mechanics of classical particles with logarithmic interactions; Commun. Pure Appl. Math. 46 (1993), 27-56. Zbl0811.76002MR1193342
- [43] F. King, PhD Thesis, U. of California, Berkeley 1975.
- [44] L. Landau, E. Lifshitz: Mécanique quantique; Editions Mir, Moscou 1967.
- [45] L. Landau, E. Lifshitz: Théorie quantique relativiste, première partie; Editions Mir, Moscou 1972. MR389019
- [46] L. Landau, E. Lifshitz: Physique statistique, deuxième partie; Editions Mir, Moscou 1990.
- [47] O. Lanford: Time evolution of large classical systems, in ``Dynamical systems, theory and applications" (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), pp. 1-111. Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975. Zbl0329.70011MR479206
- [48] C. Marchioro, M. PulvirentiMathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag (1994). Zbl0789.76002MR1245492
- [50] V. Maslov: Equations of the self-consistent field; J. Soviet Math. 11 (1979), 123-195. Zbl0408.45010MR489604
- [51] H. Narnhofer, G.L. Sewell, Vlasov hydrodynamics of a quantum mechanical model, Comm. Math. Phys. 79 (1981), 9-24. MR609224
- [52] H. NeunzertThe Vlasov equation as a limit of Hamiltonian classical mechanical systems of interacting particles; Trans. Fluid Dynamics 18 (1977), 663-678.
- [52] L. NirenbergAn abstract form of the nonlinear Cauchy-Kowalewski theorem; J. Differential Geometry 6 (1972), 561-576. Zbl0257.35001MR322321
- [53] L. OnsagerStatistical hydrodynamics, Supplemento al Nuovo Cimento 6 (1949), 279-287. MR36116
- [54] T. NishidaA note on a theorem of Nirenberg; J. Differential Geometry 12 (1977), 629-633. Zbl0368.35007MR512931
- [55] H. Spohn, Kinetic Equations from Hamiltonian Dynamics: Markovian Limits, Rev. Modern Phys. 52 (1980), 569-615. MR578142
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.