Mean field dynamics of fermions and the time-dependent Hartree–Fock equation
Tài liệu tham khảo
Alicki, 1983, Nonlinear quantum dynamical semigroups for many-body open systems, J. Statist. Phys., 32, 299, 10.1007/BF01012712
Bardos, 2000, Weak coupling limit of the N-particle Schrödinger equation, Math. Anal. Appl., 7, 275, 10.4310/MAA.2000.v7.n2.a2
Bardos, 2002, Derivation of the Schrödinger–Poisson equation from the quantum N-particle Coulomb problem, C. R. Acad. Sci., 10.1016/S1631-073X(02)02253-7
Boltzmann, 1995
Bove, 1974, An existence proof for the Hartree–Fock time-dependent problem with bounded two-body interaction, Comm. Math. Phys., 37, 183, 10.1007/BF01646344
Cances, 1999, On the time-dependent Hartree–Fock equations coupled with a classical nuclear dynamics, Math. Models Methods Appl. Sci., 9, 963, 10.1142/S0218202599000440
Duffield, 1992, Local dynamics of mean-field quantum systems, Helv. Phys. Acta, 65, 1016
L. Erdös, H.-T. Yau, Derivation of the nonlinear Schrödinger equation with Coulomb potential, Preprint, 2002
A.D. Gottlieb, Markov transitions and the propagation of chaos, PhD Thesis, Lawrence Berkeley National Laboratory Report, LBNL-42839, 1998
Grünbaum, 1971, Propagation of chaos for the Boltzmann equation, Arch. Rational Mech. Anal., 42, 323, 10.1007/BF00250440
Kac, 1956, Foundations of kinetic theory
Kac, 1976
McKean, 1966, A class of Markov processes associated with nonlinear parabolic equations, Proc. Nat. Acad. Sci., 56, 1907, 10.1073/pnas.56.6.1907
Méléard, 1995, Asymptotic behavior of some interacting particle systems; McKean–Vlasov and Boltzmann models, 1627
Spohn, 1980, Kinetic equations from Hamiltonian dynamics, Rev. Mod. Phys., 53, 600
Sznitman, 1984, Équations de type de Boltzmann, spatialement homogènes, Z. Wahrscheinlichkeitsth., 66, 559, 10.1007/BF00531891
Sznitman, 1991, 1464