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All issues Volume 48 / No 1 (January-February 2014) ESAIM: M2AN, 48 1 (2014) 53-86 References
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Issue
ESAIM: M2AN
Volume 48, Number 1, January-February 2014
Page(s) 53 - 86
DOI https://doi.org/10.1051/m2an/2013094
Published online 15 November 2013
  1. H. Attouch and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. 116 (2009) 5–16. [Google Scholar]
  2. V. Bach, Error bound for the Hartree-Fock energy of atoms and molecules. Commun. Math. Phys. 147 (1992) 527–548. [CrossRef] [Google Scholar]
  3. V. Bach, J. Fröhlich and L. Jonsson, Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions. J. Math. Phys. 50 (2009) 22. [CrossRef] [Google Scholar]
  4. V. Bach, E.H. Lieb and J.Ph. Solovej, Generalized Hartree-Fock theory and the Hubbard model. J. Statist. Phys. 76 (1994) 3–89. [Google Scholar]
  5. J. Bardeen, L.N. Cooper and J.R. Schrieffer, Theory of superconductivity. Phys. Rev. 108 (1957) 1175–1204. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. L. Baudouin and J. Salomon, Constructive solution of a bilinear optimal control problem for a Schrödinger equation. Syst. Cont. Lett. 57 (2008) 453–464. [CrossRef] [Google Scholar]
  7. P. Billard and G. Fano, An existence proof for the gap equation in the superconductivity theory. Commun. Math. Phys. 10 (1968) 274–279. [Google Scholar]
  8. N.N. Bogoliubov, About the theory of superfluidity. Izv. Akad. Nauk SSSR 11 (1947) 77. [Google Scholar]
  9. N.N. Bogoliubov, Energy levels of the imperfect Bose gas. Bull. Moscow State Univ. 7 (1947) 43. [Google Scholar]
  10. N.N. Bogoliubov, On the theory of superfluidity. J. Phys. (USSR) 11 (1947) 23. [Google Scholar]
  11. N.N. Bogoliubov, On a New Method in the Theory of Superconductivity. J. Exp. Theor. Phys. 34 (1958) 58. [Google Scholar]
  12. J. Bolte, A. Daniilidis, O. Ley and L. Mazet, Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity. Trans. Amer. Math. Soc. 362 (2010) 3319–3363. [Google Scholar]
  13. É. Cancès, SCF algorithms for HF electronic calculations, in Mathematical models and methods for ab initio quantum chemistry, vol. 74, in Lect. Notes Chem., Chapt. 2. Springer, Berlin (2000) 17–43. [Google Scholar]
  14. É. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris and Y. Maday, Computational quantum chemistry: a primer, in Handbook of numerical analysis, vol. X, Handb. Numer. Anal. North-Holland, Amsterdam (2003) 3–270. [Google Scholar]
  15. É. Cancès and C. Le Bris, Can we outperform the DIIS approach for electronic structure calculations? Int. J. Quantum Chem. 79 (2000) 82–90. [CrossRef] [Google Scholar]
  16. É. Cancès and C. Le Bris, On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM: M2AN 34 (2000) 749–774. [CrossRef] [EDP Sciences] [Google Scholar]
  17. É. Cancès, C. Le Bris and Y. Maday, Méthodes mathématiques en chimie quantique. Une introduction, vol. 53 of Collection Mathématiques et Applications. Springer (2006). [Google Scholar]
  18. E.B. Davies, Spectral theory and differential operators, vol. 42, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1995). [Google Scholar]
  19. J. Dechargé and D. Gogny, Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei. Phys. Rev. C 21 (1980) 1568–1593. [CrossRef] [Google Scholar]
  20. C. Fefferman and R. de la Llave, Relativistic stability of matter. I. Rev. Mat. Iberoamericana 2 (1986) 119–213. [CrossRef] [MathSciNet] [Google Scholar]
  21. R.L. Frank, C. Hainzl, R. Seiringer and J.P. Solovej, Microscopic Derivation of Ginzburg-Landau Theory. J. Amer. Math. Soc. 25 (2012) 667–713. [Google Scholar]
  22. R.L. Frank, C. Hainzl, S. Naboko and R. Seiringer, The critical temperature for the BCS equation at weak coupling. J. Geom. Anal. 17 (2007) 559–567. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Friesecke, The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions. Arch. Ration. Mech. Anal. 169 35–71 (2003). [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Gogny, in Proceedings of the International Conference on Nuclear Physics, edited by J. de Boer and H.J. Mang. (1973) 48. [Google Scholar]
  25. D. Gogny, in Proceedings of the International Conference on Nuclear Self-Consistent Fields, edited by M. Porneuf and G. Ripka. Trieste (1975) 333. [Google Scholar]
  26. D. Gogny and P.-L. Lions, Hartree-Fock theory in nuclear physics. RAIRO Modél. Math. Anal. Numér. 20 (1986) 571–637. [Google Scholar]
  27. C. Hainzl, E. Hamza, R. Seiringer and J.P. Solovej, The BCS functional for general pair interactions. Commun. Math. Phys. 281 (2008) 349–367. [CrossRef] [Google Scholar]
  28. C. Hainzl, E. Lenzmann, M. Lewin and B. Schlein, On blowup for time-dependent generalized Hartree-Fock equations. Annal. Henri Poincaré 11 (2010) 1023–1052. [Google Scholar]
  29. C. Hainzl and R. Seiringer, General decomposition of radial functions on Rn and applications to N-body quantum systems. Lett. Math. Phys. 61 (2002) 75–84. [CrossRef] [Google Scholar]
  30. C. Hainzl and R. Seiringer, The BCS critical temperature for potentials with negative scattering length. Lett. Math. Phys. 84 (2008) 99–107. [CrossRef] [Google Scholar]
  31. M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, Schrödinger inequalities and asymptotic behavior of the electron density of atoms and molecules. Phys. Rev. A 16 (1977) 1782–1785. [CrossRef] [Google Scholar]
  32. T. Kato, Perturbation theory for linear operators. Springer (1995). [Google Scholar]
  33. C. Le Bris, Computational chemistry from the perspective of numerical analysis. Acta Numerica 14 (2005) 363–444. [CrossRef] [MathSciNet] [Google Scholar]
  34. E. Lenzmann and M. Lewin, Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs. Duke Math. J. 152 (2010) 257–315. [CrossRef] [Google Scholar]
  35. A. Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations. ESAIM: M2AN 46 (2012) 1321–1336. [CrossRef] [EDP Sciences] [Google Scholar]
  36. M. Lewin, Geometric methods for nonlinear many-body quantum systems. J. Funct. Anal. 260 (2011) 3535–3595. [CrossRef] [MathSciNet] [Google Scholar]
  37. E.H. Lieb, Variational principle for many-fermion systems. Phys. Rev. Lett. 46 (1981) 457–459. [CrossRef] [Google Scholar]
  38. E.H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics. Cambridge Univ. Press (2010). [Google Scholar]
  39. E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53 (1977) 185–194. [CrossRef] [MathSciNet] [Google Scholar]
  40. E.H. Lieb and W.E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy. Annal. Phys. 155 (1984) 494–512. [CrossRef] [Google Scholar]
  41. E.H. Lieb and H.-T. Yau, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics. Commun. Math. Phys. 112 (1987) 147–174. [CrossRef] [Google Scholar]
  42. P.-L. Lions, Solutions of Hartree-Fock equations for Coulomb systems. Commun. Math. Phys. 109 (1987) 33–97. [CrossRef] [MathSciNet] [Google Scholar]
  43. S. Łojasiewicz, Une propriété topologique des sous-ensembles analytiques réels. Colloques du CNRS, Les équations aux dérivés partielles (1963) 117. [Google Scholar]
  44. S. Łojasiewicz, Sur la géométrie semi- et sous-analytique. Ann. Inst. Fourier (Grenoble) 43 (1993) 1575–1595. [CrossRef] [Google Scholar]
  45. J.B. McLeod and Y. Yang, The uniqueness and approximation of a positive solution of the Bardeen-Cooper-Schrieffer gap equation. J. Math. Phys. 41 (2000) 6007–6025. [CrossRef] [Google Scholar]
  46. S. Paul, Modèle de Hartree-Fock-Bogoliubov : une perspective mathématique et numérique. Ph.D. thesis, Univ. Cergy-Pontoise (2012). [Google Scholar]
  47. P. Quentin and H. Flocard. Self-Consistent Calculations of Nuclear Properties with Phenomenological Effective Forces. Ann. Rev. Nucl. Part. Sci. 28 (1978) 523–594. [Google Scholar]
  48. P. Ring and P. Schuck, The nuclear many-body problem, volume Texts and Monographs in Physics. Springer Verlag, New York (1980). [Google Scholar]
  49. C.C.J. Roothaan, New developments in molecular orbital theory. Rev. Mod. Phys. 23 (1951) 69–89. [CrossRef] [Google Scholar]
  50. J. Salomon, Convergence of the time-discretized monotonic schemes. ESAIM: M2AN 41 (2007) 77–93. [CrossRef] [EDP Sciences] [Google Scholar]
  51. S. Consortium, Scilab: The free software for numerical computation. Scilab Consortium, Digiteo, Paris, France (2011). [Google Scholar]
  52. B. Simon, Geometric methods in multiparticle quantum systems. Commun. Math. Phys. 55 (1977) 259–274. [CrossRef] [Google Scholar]
  53. T.H.R. Skyrme. The effective nuclear potential. Nuclear Phys. 9 (1959) 615–634. [Google Scholar]
  54. J.Ph. Solovej, Proof of the ionization conjecture in a reduced Hartree-Fock model. Invent. Math. 104 (1991) 291–311. [CrossRef] [MathSciNet] [Google Scholar]
  55. J.Ph. Solovej, The ionization conjecture in Hartree-Fock theory. Annal. Math. 158 (2003) 509–576. [CrossRef] [Google Scholar]
  56. A. Vansevenant, The gap equation in superconductivity theory. Phys. D 17 (1985) 339–344. [CrossRef] [MathSciNet] [Google Scholar]
  57. Y.S. Yang, On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity. Lett. Math. Phys. 22 (1991) 27–37. [CrossRef] [MathSciNet] [Google Scholar]

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