Estimations exponentielles en théorie de la diffusion pour des opérateurs de Schrödinger matriciels

Mohammed Benchaou; André Martinez

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 6, page 561-594
  • ISSN: 0246-0211

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Benchaou, Mohammed, and Martinez, André. "Estimations exponentielles en théorie de la diffusion pour des opérateurs de Schrödinger matriciels." Annales de l'I.H.P. Physique théorique 71.6 (1999): 561-594. <http://eudml.org/doc/76845>.

@article{Benchaou1999,
author = {Benchaou, Mohammed, Martinez, André},
journal = {Annales de l'I.H.P. Physique théorique},
language = {fre},
number = {6},
pages = {561-594},
publisher = {Gauthier-Villars},
title = {Estimations exponentielles en théorie de la diffusion pour des opérateurs de Schrödinger matriciels},
url = {http://eudml.org/doc/76845},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Benchaou, Mohammed
AU - Martinez, André
TI - Estimations exponentielles en théorie de la diffusion pour des opérateurs de Schrödinger matriciels
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 6
SP - 561
EP - 594
LA - fre
UR - http://eudml.org/doc/76845
ER -

References

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  2. [2] C. Gérard and A. Martinez, Principe d'absorption limite pour des opérateurs de Schrödinger à longue porté, C. R. Acad. Sci. Paris906 I (1988) 121-123. Zbl0672.35013MR929103
  3. [3] B. Helffer and J. Sjöstrand, Equation de Schrödinger avec champ magnétique et équation de Harper, Lecture Notes in Physics, vol. 345, Springer, Berlin, 1989, 118-197. Zbl0699.35189MR1037319
  4. [4] H. Isozaki, Decay rates of scattering states for Schrödinger operators, J. Math. Kyoto Univ.26 (1986) 595-603. Zbl0622.35055MR864463
  5. [5] T. Jecko, Sections efficaces totales d'une molécule diatomique dans l'approximation de Born-Oppenheimer, Thèse de Doctorat, Université de Nantes, 1996. 
  6. [6] A. Jensen and S. Nakamura, Mapping properties for wave and scattering operators for two-body Schrödinger operators, Lett. Math. Phys.24 (1992) 295- 305. Zbl0761.35074MR1172457
  7. [7] K. Jung, Adiabatik und Semiklassik bei Regularität vom Gevrey-Typ, Ph.D. Thesis, Technische Universität Berlin, 1997. 
  8. [8] M. Klein, A. Martinez and X.P. Wang, On the Born-Oppenheimer approximation of wave operators, Comm. Math. Phys.152 (1993). Zbl0778.35088
  9. [9] M. Klein, A. Martinez and X.P. Wang, On the Born—Oppenheimer approximation of wave operators II: Singular potentials, J. Math. Phys.38 (3) (1997) 1373- 1396. Zbl0874.35103MR1435674
  10. [10] M. Klein, A. Martinez, R. Seiler and X.P. Wang, On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys.143 (1992). Zbl0754.35099MR1145603
  11. [11] A. Martinez, Estimates on complex interactions in phase space, Math. Nachr.167 (1994) 203-254. Zbl0836.35135MR1285313
  12. [12] A. Martinez, Precise exponential estimates in adiabatic theory, J. Math. Phys.35 (8) (1994) 3889-3915. Zbl0808.47053MR1284618
  13. [13] A. Melin and J. Sjöstrand, Fourier integral operators with complex-valued phase functions, Lecture Notes in Math., vol. 459, Springer, Berlin, 1975, 120- 223. Zbl0306.42007MR431289
  14. [14] E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys.78 (1981) 391-408. Zbl0489.47010MR603501
  15. [15] S. Nakamura, On an example of phase-space tunneling, Ann. Inst. H. Poincaré, 63 (2) (1995). Zbl0833.34088MR1357496
  16. [16] S. Nakamura, On Martinez' method of phase space tunneling, Rev. Math. Phys.7 (3) (1995) 431-441. Zbl0842.35145MR1326141
  17. [17] S. Nakamura, Tunneling effects in momentum space and scattering, in: M. Ikawa (Ed.), Spectral and Scattering Theory, Lecture Notes in Pure Appl. Math., vol. 161, Marcel Decker, New York, 1994. Zbl0827.35097MR1291641
  18. [18] M. Reed and B. S Imon, Methods of Modern Mathematical Physics, Academic Press, 1972. 
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  21. [21] X.P. Wang, Time-decay of scattering solutions and resolvent estimates for semiclassical Schrödinger operators, J. Differential Equations71 (1988) 348-395. Zbl0651.35022MR927007

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