Résonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension deux

 Access to full text

 Full (PDF)

1. [AC71] J. Aguilar et J.M. Combes, A class of analytic pertubations for one body Schrödinger Hamiltonians, Commun. Math. Phys., Vol. 22, 1971, p. 269-279. Zbl0219.47011MR345551
2. [BCD85] Ph Briet, J.M. Combes et P. Duclos, On the location of resonances for Schrödinger operators in the semiclassical limit I, J. Math. Anal. Appl., Nov. 1985. Zbl0629.47043
3. [BCD87] Ph Briet, J.M. Combes et P. Duclos, On the location of resonances for Schrödinger operators in the semiclassical limit II, Comm. Part. Diff. Eq., Vol. 12, 1987, p. 209-258. Zbl0622.47047
4. [CDS81] J.M. Combes, P. Duclos et R. Seiler, The Born Oppenheimer approximation , Rigorous Atomic and molecular, Physic, 1981, p. 185-212. 
5. [Fed83] M.V. Fedoryuk, Asymptotic analysis, 1983, Springer verlag. MR1295032
6. [GS94] A. Grigis et J. Sjöstrand, Microlocal analysis for diff. op., 1994, Cambridge Univ. Press. MR1269107
7. [Hag90] G.A. Hagedorn, Electron energy level crossing in time dependent Born Oppenheimer approximation, Theoretica Chimica Acta., Vol. 77, 1990, p. 163-190. 
8. [Hag94] G.A. Hagedorn, Molecular propagation through electron energy level crossings, Memoirs A.M.S. 536, Vol. 111, 1994. Zbl0833.92025MR1234882
9. [HeSi81] I. Herbst et B. Simon, Dilation analyticity in constant electric field II. The N-body problem, Borel summability, Commun. Math. Phys., Vol. 80, 1981, p. 181-216. Zbl0473.47038MR623157
10. [HS84] B. Helffer et J. Sjöstrand, Multiple wells in the semi classical limit I, Communication in partial differential equations, Vol. 9 (5), 1984. Zbl0546.35053
11. [HS86] B. Helffer et J. Sjöstrand, Résonances en limite semi-classique, Mémoire de la S.M.F., 1986. Zbl0631.35075
12. [HS89] B. Helffer et J. Sjöstrand, Semi classical analysis for Harper's aquation III, Mémoire de la S.M.F., 1989. Zbl0725.34099
13. [HS90] B. Helffer et J. Sjöstrand, Analyse semi-classique pour l'équation de Harper II, Mémoire de la S.M.F., Vol. 40,1990. Zbl0714.34131
14. [Hun86] W. Hunziker, Distorsion analyticity and molecular resonances curves, Annales de l'I.H.P., mars1986. 
15. [Joy94] A. Joye, Proof of the landau-zener formula, Asympt. Anal., Vol. 9, 1994, p. 209-258. Zbl0814.35109MR1295294
16. [Kat76] Kato, Perturbation theory for linear operators, Springer, 1976. MR407617
17. [Kle87] M. Klein, On the mathematical theory of predissociation, Ann. of Physics, Vol. 178 (1), 1987, p. 48-73. Zbl0649.35024MR913151
18. [KMSW92] M. Klein, A. Martinez, R. Seiler et X.P. Wang, On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys., Vol. 143, 1992, p. 607-639. Zbl0754.35099MR1145603
19. [KR93] N. Kaïdi et M. Rouleux, Forme normale d'un hamiltonien à 2 niveaux près d'un point de branchement.Limite semi-classique, C.R.A.S., Vol. 317, série I, 1993, p. 359-364. Zbl0797.58083MR1235449
20. [Lau85] P. Laubin, Hyperbolic boundary value problems..., Proc. Nato asi on adv in Microl. anal., 1985, p. 165-202. MR850502
21. [Mä92] C. März, Spectral asymptotics for Hill's equation near the potential maximum, Asymptotic Analysis, Vol. 5, 1992, p. 221-267. Zbl0786.34080MR1145112
22. [Mar91a] A. Martinez, Résonances dans l'approximation de Born Oppenheimer I, Journal of Differ. Eq., 1991, p. 204-234. Zbl0737.35046MR1111174
23. [Mar91b] A. Martinez, Résonances dans l'approximation de Born Oppenheimer II. Largeur des résonances, Commun. Math. Phys., Vol. 135, 1991, p. 517-530. Zbl0737.35047MR1091576
24. [Mes93] B. Messirdi, Asymptotique de Born-Oppenheimer pour la prédissociation moléculaire (cas des potentiels réguliers), Annales de l'I.H.P., physique théorique, Vol. 61, 1993, p. 255-292. Zbl0812.35109MR1311068
25. [Nak94a] S. Nakamura, On an example of phase space tunneling, à paraître, 1994. MR1357496
26. [Nak94b] S. Nakamura, Tunneling effects in momentum space and scattering, à paraître, 1994. Zbl0827.35097MR1291641
27. [Pet93] P. Pettersson, W.K.B expansions for systems of Schrödinger operators with crossing eigenvalues, PhD thesis, University of Lund, 1993. 
28. [Sim83] B. Simon, Semi-classical analysis of low lying eigenvalues I. Non degenerate minima : asymptotic expensions, Ann. Inst. Henri Poincaré, Vol. 38, 1983, p. 295-307. Zbl0526.35027MR708966
29. [Sj80] J. Sjöstrand, Problèmes aux limites microhyperboliques, Math. Analy., 1980. 
30. [Sj82] J. Sjöstrand, Singularités analytiques microlocales, Vol. 95, Astérisque, 1982. Zbl0524.35007MR699623
31. [SW89] A. Shapere et F. Wilczek, Geometric phases in physics, World Sci., 1989. Zbl0914.00014MR1084385

1. M. Rouleux, Résonances de Feschbach en limite semi-classique