Résonances de Feschbach en limite semi-classique

M. Rouleux

Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996)

  • page 1-11

How to cite

top

Rouleux, M.. "Résonances de Feschbach en limite semi-classique." Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996): 1-11. <http://eudml.org/doc/112130>.

@article{Rouleux1995-1996,
author = {Rouleux, M.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
language = {fre},
pages = {1-11},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Résonances de Feschbach en limite semi-classique},
url = {http://eudml.org/doc/112130},
year = {1995-1996},
}

TY - JOUR
AU - Rouleux, M.
TI - Résonances de Feschbach en limite semi-classique
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1995-1996
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 11
LA - fre
UR - http://eudml.org/doc/112130
ER -

References

top
  1. [Ba] H. BakloutiAsymptotique des largeurs de résonances pour un modèle d'effet tunnel microlocal microlocal. Thèse U. Paris Nord, 1995 
  2. [Be] M.V. Berry 1. Quantal phase factors accompying adiabatic changes. Proc. R. Soc. London A 1984. p. 45-57. (reprinted in [ShWi]) 2. Asymptotics, Superasymptotics, Hyperasymptotics, in: Asymptotics beyond all orders. Segur, ed. Plenum PressN.Y. 1991. Zbl1113.81306MR738926
  3. [CdVPa] Y. Colin de Verdière B.Parisse 1. Equilibre instable en régime semi-classique I. Concentration microlocale. Comm. Part. Diff.Eq. 252, 1993. 2. Equilibre instable en régime semi-classique II. Conditions de Bohr Sommerfeld. Ann. Inst. H. Poincaré. Phys. Théorique. 61(3) 1994. p.347-367 Zbl0845.35076MR1311072
  4. [CoDuSe] J.M. Combes P. Duclos R. SeilerThe Born-Oppenheimer approximation, in: Rigorous atomic and Molecular Physics, Velo and Wightman, eds. Plenum Press, 1981, p.185-212. 
  5. [DeDi] E. Delabaere H.Dillinger Contribution á la résurgence quantique. Thèse. U. Nice, 1991 
  6. [DuMe] P. Duclos B.Meller A simple model for predissociation, in: Operator Theory: Advances and Applications. Vol. 70, Birkhäuser. Zbl0831.47005MR1309010
  7. [Gr] A. GrigisRésonances par correspondance. Séminaire EdP, Ecole Polytechnique. 1994-95 Exposé no 23 Zbl0881.35100MR1362571
  8. [GrSj] A. Grigis J.Sjöstrand Microlocal Analysis for Differential Operators.Cambridge University Press1994. Zbl0804.35001MR1269107
  9. [Ha] G. HagedornMolecular propagation through electron energy level crossings. Memoirs A.M.S. 536, 111, 1994 Zbl0833.92025MR1234882
  10. [HaJo] G. Hagedorn A. JoyeLandau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation. Preprint CPT-95/P. 3215, 1995. 
  11. [HeSj] B. Helffer J. Sjöstrand1. Résonances en limite semi-classique. Bull. Soc. Math. France114(3) 1986. Mémoire no 24/25. 2. Semiclassical analysis for Harper equation III. Cantor structure of the spectrum. Bull. Soc. Math. France117(4) 1989. Mémoire no 39. Zbl0631.35075MR871788
  12. [HeMa] B. Helffer A.Martinez Comparaison entre les diverses notions de résonances. Helv. Phys. Acta60, 1987 p.992-1008 MR929933
  13. [Hu] W. HunzikerDistorsion analyticity and molecular resonances curves. Ann. I. H. P. Phys. Th.45(3), 1986 p.485-494 Zbl0619.46068MR880742
  14. [Iv] V. IvrïiSemiclassical Microlocal Analysis and Precise Spectral Asymptotics. Preprint Ecole Polytechnique, 1990, disponible aussi par: ftp://www.scar.toronto.edu/pub/math.preprints/ivrii/Book. Zbl0906.35003MR1631419
  15. [JaSe] V. Jakšić J. SegertExponential approach to the adiabatic limit and the Landau-Zener formula. Preprint Caltech, 1994. Zbl0769.34006MR1197550
  16. [Jo] A. JoyeProof of the Landau-Zener formula. Asympt. Anal.9(3), 1994 p.202-259 [KaRo] N. Kaïdi M. RouleuxForme normale d'un hamiltonien à 2 niveaux près d'un point de branchement (limite semi-classique.)C.R. Acad. Sci. ParisI1171993. p.359-364 Zbl0814.35109MR1295294
  17. [KlMaWa] M. Klein A. Martinez X.P. WangOn the Born-Oppenheimer approximation of wave operators in molecular scattering theory. Comm. Math. Physics, 152, 1993, p.73-95 Zbl0778.35088MR1207670
  18. [KIMaSeWa] M. Klein A. Martinez R. Seiler X.P. WangOn the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Physics, 143, 1992, p.606-639 Zbl0754.35099MR1145603
  19. [Ko] J. Korsch Semiclassical description of resonances, in: Resonances, Brändas Elander, eds, Lect. Notes Phys. 325, Springer, 1989 p.253-280 MR1022494
  20. [LaLi] L. Landau E. LifchitzPhysique Théorique. Mécanique Quantique, Mir, 1967. Zbl0144.47605
  21. [Ma] A. Martinez 1. Résonances dans l'approximation de Born-Oppenheimer. J.of Diff. Eq. 91, 1991, p.517-530. 2. Estimates on complex interactions in phase space. Math. Nachr.167, 1994 p.203-257 Zbl0737.35046
  22. [MaMes] A. Martinez B. MessirdiResonances of diatomic molecules in the Born- Oppenheimer approximation. Comm. Part. Diff. Eq. 19 (7 et 8), 1994, p.1139-1162 Zbl0826.35148MR1284804
  23. [Mä] Ch. MärzSpectral asymptotics for Hill's equation near the potential maximum. Asymptotic Anal.51992, p.221-267 Zbl0786.34080MR1145112
  24. [Me] B. MellerThèseU. Toulon, 1995 
  25. [MöKo] R. Möhlenkamp J. KorschSemi-classical complex energy quantization for coupled equations: Feshbach resonances and predissociation. Phys. Rev.A34(6), 1986 p.4717-4721 
  26. [Na] S. NakamuraOn an example of phase-space tunneling. Ann. I.H. P. Phys. Th. 63(2), 1995, p.211-229 Zbl0833.34088MR1357496
  27. [N] L. NedelecRésonances semi-classiques pour l'opérateur de Schrödinger matriciel en dimension 2. Ann. I.H P. Phys. Th. 1995 Zbl0915.35091
  28. [Ra] A. RaphaelianIon-atom scattering within a Born-Oppenheimer framework. Dissertation T.U. Berlin, 1986. 
  29. [Ro] M. RouleuxFeshbach resonances in the semi-classical limit. Preprint CPT/P.3230, 1995 
  30. [ShWi] A. Shapere F.Wilczek Geometric Phases in Physics. World Scientific, Vol 5, 1989 Zbl0914.00014MR1084385
  31. [Sj] J. Sjöstrand 1. Singularités analytiques microlocales. Astérisque951982. 2. Density of states oscillations for Magnetic Schrödinger operators. In: Bennewitz (ed.) Differential Equations and Mathematical Physics 1990. Univ. of Alabama, Birmingham. p.295-345 3. Function spaces associated to global I-lagrangian manifolds. Preprint Ecole Polytechnique no 1111, 1995. Zbl0524.35007MR699623
  32. [So] V. SordoniBorn-Oppenheimer expansion for excited states of diatomic molecules. C. R. Acad. Sc. Paris I, 320, 1994 p.1091-1096 Zbl0827.35111MR1332617

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.