Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation

Bernard Ducomet

Applications of Mathematics (2010)

  • Volume: 55, Issue: 3, page 197-219
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Ducomet, Bernard. "Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation." Applications of Mathematics 55.3 (2010): 197-219. <http://eudml.org/doc/37844>.

@article{Ducomet2010,
abstract = {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.},
author = {Ducomet, Bernard},
journal = {Applications of Mathematics},
keywords = {time-dependent Hartree-Fock equation; nuclear matter; time-dependent Hartree-Fock equation; nuclear matter},
language = {eng},
number = {3},
pages = {197-219},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation},
url = {http://eudml.org/doc/37844},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Ducomet, Bernard
TI - Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 197
EP - 219
AB - 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.
LA - eng
KW - time-dependent Hartree-Fock equation; nuclear matter; time-dependent Hartree-Fock equation; nuclear matter
UR - http://eudml.org/doc/37844
ER -

References

top
  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). (1977) MR0495999
  2. Bardos, C., Golse, F., Mauser, N. J., Weak coupling limit of the N -particle Schrödinger equation, Methods Appl. Anal. 7 (2000), 275-293. (2000) Zbl1003.81027MR1869286
  3. Bardos, C., Golse, F., Gottlieb, A. D., Mauser, N. J., 10.1016/S0021-7824(03)00023-0, J. Math. Pures Appl., IX. Sér. 82 (2003), 665-683. (2003) Zbl1029.82022MR1996777DOI10.1016/S0021-7824(03)00023-0
  4. Bardos, C., Ducomet, B., Golse, F., Gottlieb, A. D., Mauser, N. J., 10.4310/CMS.2007.v5.n5.a2, Commun. Math. Sci. 1 (2007), 1-9. (2007) MR2301285DOI10.4310/CMS.2007.v5.n5.a2
  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., 10.1016/S1631-073X(02)02253-7, C. R., Math. Acad. Sci. Paris 334 (2002), 515-520. (2002) MR1890644DOI10.1016/S1631-073X(02)02253-7
  7. Beiner, M., Flocard, H., Giai, N. Van, Quentin, P., 10.1016/0375-9474(75)90338-3, Nucl. Phys. A238 (1975), 29-69. (1975) DOI10.1016/0375-9474(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). (1996) 
  9. Bove, A., Prato, G. Da, Fano, G., 10.1007/BF01608633, Commun. Math. Phys. 49 (1976), 25-33. (1976) MR0456066DOI10.1007/BF01608633
  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). (1992) 
  11. Chabanat, E., Bonche, P., Haensel, P., Meyer, J., Schaeffer, R., 10.1016/S0375-9474(97)00596-4, Nucl. Phys. A627 (1997), 710-746. (1997) DOI10.1016/S0375-9474(97)00596-4
  12. Dechargé, J., Gogny, D., 10.1103/PhysRevC.21.1568, Phys. Rev. C 21 (1980), 1568-1593. (1980) DOI10.1103/PhysRevC.21.1568
  13. Ducomet, B., Weak interaction limit for a model of nuclear matter, Oberwolfach Reports No 47 (2006), 2819-2822. (2006) 
  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. MR1926667
  15. Fetter, A. L., Walecka, J. D., Quantum Theory of Many-Particle Systems, McGraw Hill New York (1971). (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). (2003) MR2050595
  17. Kato, T., Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Am. Math. Soc. 70 (1951), 195-211. (1951) Zbl0044.42701MR0041010
  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., 10.1051/m2an/1986200405711, RAIRO, Modélisation Math. Anal. Numér. 20 (1986), 571-637. (1986) Zbl0607.35078MR0877058DOI10.1051/m2an/1986200405711
  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). (1980) MR0611683
  22. Serot, B. D., Walecka, J. D., The Relativistic Nuclear Many-body Problem. Adv. Nucl. Phys. 16, Plenum New York (1986). (1986) 
  23. Spohn, H., Kinetic equations from Hamiltonian dynamics, Rev. Mod. Phys. 53 (1980), 600-640. (1980) Zbl0465.76069
  24. Vautherin, D., Brink, D. M., 10.1103/PhysRevC.5.626, Phys. Rev. C 5 (1972), 626-647. (1972) DOI10.1103/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. (1968) MR0260334
  26. Winter, C. Van, Brascamp, H. J., The N -body problem with spin-orbit or Coulomb interactions, Comm. Math. Phys. 11 (1968), 19-55. (1968) MR0260334

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.