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Article

Keywords:
time-dependent Hartree-Fock equation; nuclear matter
Summary:
We consider an effective model of nuclear matter including spin and isospin degrees of freedom, described by an $N$-body Hamiltonian with suitably renormalized two-body and three-body interaction potentials. We show that the corresponding mean-field theory (the time-dependent Hartree-Fock approximation) is ``exact'' as $N$ tends to infinity.
References:
[1] Amrein, W. O., Jauch, J. M., Sinha, K. B.: Scattering Theory in Quantum Mechanics. Lecture Notes and Supplements in Physics, 16. W. A. Benjamin London (1977). MR 0495999
[2] Bardos, C., Golse, F., Mauser, N. J.: Weak coupling limit of the $N$-particle Schrödinger equation. Methods Appl. Anal. 7 (2000), 275-293. MR 1869286 | Zbl 1003.81027
[3] Bardos, C., Golse, F., Gottlieb, A. D., Mauser, N. J.: Mean field dynamics of fermions and the time-dependent Hartree-Fock equation. J. Math. Pures Appl., IX. Sér. 82 (2003), 665-683. DOI 10.1016/S0021-7824(03)00023-0 | MR 1996777 | Zbl 1029.82022
[4] Bardos, C., Ducomet, B., Golse, F., Gottlieb, A. D., Mauser, N. J.: The TDHF approximation for Hamiltonians with $m$-particle interaction potentials. Supplement. Commun. Math. Sci. 1 (2007), 1-9. DOI 10.4310/CMS.2007.v5.n5.a2 | MR 2301285
[5] Bardos, C., Golse, F., Gottlieb, A. D., Mauser, N. J.: Derivation of the time dependent Hartree-Fock equation with Coulomb potential. Preprint.
[6] Bardos, C., Erdős, L., Golse, F., Mauser, N. J., Yau, H.-T.: Derivation of the Schrödinger-Poisson equation from the quantum $N$-body problem. C. R., Math. Acad. Sci. Paris 334 (2002), 515-520. DOI 10.1016/S1631-073X(02)02253-7 | MR 1890644
[7] Beiner, M., Flocard, H., Giai, N. Van, Quentin, P.: Nuclear ground-state properties and self-consistent calculations with the skyrme interaction: I. Spherical description. Nucl. Phys. A238 (1975), 29-69. DOI 10.1016/0375-9474(75)90338-3
[8] Bitaud, L.: Etude théorique de la fission des transactinides dans le cadre d'une approche microscopique. PhD. Thesis Université Paris-Sud Paris (1996).
[9] Bove, A., Prato, G. Da, Fano, G.: On the Hartree-Fock time-dependent problem. Commun. Math. Phys. 49 (1976), 25-33. DOI 10.1007/BF01608633 | MR 0456066
[10] Catto, I.: Some remarks on Hartree-type models in nuclear physics. In: Analyse mathématique de modèles de la Mécanique Quantique. PhD. Thesis Université Paris-Dauphine Paris (1992).
[11] Chabanat, E., Bonche, P., Haensel, P., Meyer, J., Schaeffer, R.: A Skyrme parametrization from subnuclear to neutron star densities. Nucl. Phys. A627 (1997), 710-746. DOI 10.1016/S0375-9474(97)00596-4
[12] Dechargé, J., Gogny, D.: Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei. Phys. Rev. C 21 (1980), 1568-1593. DOI 10.1103/PhysRevC.21.1568
[13] Ducomet, B.: Weak interaction limit for a model of nuclear matter. Oberwolfach Reports No 47 (2006), 2819-2822.
[14] Erdős, L., Yau, H.-T.: Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. arXiv:math-ph/0111042v3 22 May 2002. MR 1926667
[15] Fetter, A. L., Walecka, J. D.: Quantum Theory of Many-Particle Systems. McGraw Hill New York (1971).
[16] Golse, F.: The mean-field limit for the dynamics of large particle systems. Proceedings of the conference on partial differential equations, Forges-les-Eaux, France, June 2-6, 2003 Université de Nantes Nantes (2003). MR 2050595
[17] Kato, T.: Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc. 70 (1951), 195-211. MR 0041010 | Zbl 0044.42701
[18] Knowles, A., Frölich, J.: A microscopic derivation of the time-dependent Hartree-Fock equation with Coulomb two-body interaction. arXiv:0810.4282.
[19] Lions, P.-L., Gogny, D.: Hartree-Fock theory in nuclear physics. RAIRO, Modélisation Math. Anal. Numér. 20 (1986), 571-637. DOI 10.1051/m2an/1986200405711 | MR 0877058 | Zbl 0607.35078
[20] Mornas, L.: Neutron stars in a Skyrme model with hyperons. arXiv:nucl-th/0407083 vl 23 Jul 2004.
[21] Ring, P., Schuck, P.: The Nuclear Many-Body Problem. Springer Berlin (1980). MR 0611683
[22] Serot, B. D., Walecka, J. D.: The Relativistic Nuclear Many-body Problem. Adv. Nucl. Phys. 16. Plenum New York (1986).
[23] Spohn, H.: Kinetic equations from Hamiltonian dynamics. Rev. Mod. Phys. 53 (1980), 600-640. Zbl 0465.76069
[24] Vautherin, D., Brink, D. M.: Hartree-Fock calculations with Skyrme's interaction. I. Spherical nuclei. Phys. Rev. C 5 (1972), 626-647. DOI 10.1103/PhysRevC.5.626
[25] Winter, C. Van, Brascamp, H. J.: The $N$-body problem with spin-orbit or Coulomb interactions. Comm. Math. Phys. 11 (1968), 19-55. MR 0260334
[26] Winter, C. Van, Brascamp, H. J.: The $N$-body problem with spin-orbit or Coulomb interactions. Comm. Math. Phys. 11 (1968), 19-55. MR 0260334
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