Estimations exponentielles précisées en théorie adiabatique Precise exponential estimates in adiabatic theory

André Martinez

Journées équations aux dérivées partielles (1993)

  • Volume: 1993, Issue: 6, page 1-8
  • ISSN: 0752-0360

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Martinez, André. "Estimations exponentielles précisées en théorie adiabatique." Journées équations aux dérivées partielles 1993.6 (1993): 1-8. <http://eudml.org/doc/93275>.

@article{Martinez1993,
author = {Martinez, André},
journal = {Journées équations aux dérivées partielles},
keywords = {exponential estimates; adiabatic theory},
language = {eng},
number = {6},
pages = {1-8},
publisher = {Ecole polytechnique},
title = {Estimations exponentielles précisées en théorie adiabatique},
url = {http://eudml.org/doc/93275},
volume = {1993},
year = {1993},
}

TY - JOUR
AU - Martinez, André
TI - Estimations exponentielles précisées en théorie adiabatique
JO - Journées équations aux dérivées partielles
PY - 1993
PB - Ecole polytechnique
VL - 1993
IS - 6
SP - 1
EP - 8
LA - eng
KW - exponential estimates; adiabatic theory
UR - http://eudml.org/doc/93275
ER -

References

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  2. [BoFo] M. Born, V. Fock : Beweis des Adiabatensatzes, Z. Phys. 51, p. 165-169 (1928). JFM54.0994.03
  3. [Ga] L.M. Garrido : Generalized adiabatic invariance, J. Math. Phys. 5, p. 355-362 (1964). MR29 #5547
  4. [HeSj] B. Helffer, J. Sjöstrand : Multiple Wells in the Semiclassical Limit I, Comm. P.D.E., vol. 9, (4), 1984, p. 337-408. Zbl0546.35053MR86c:35113
  5. [JaSe] V. Jakšić, J. Segert : Exponential approach to the adiabatic limit and the Landau-Zener formula, Rev. Math. Phys., Vol. 4 (4), p. 529-574 (1992). Zbl0769.34006MR94g:81040
  6. [Jo] A. Joye : Proof of the Landau-Zener Formula, Preprint C.P.T. Marseille, Dec. 1992. Zbl0814.35109
  7. [JKP] A. Joye, H. Kunz, C.-E. Pfister : Exponential Decay and Geometric Aspect of Transition Probabilities in the Adiabatic Limit, Annals of Physics 208, p. 299-332 (1991). Zbl0875.60022MR93a:81058
  8. [JoPf1] A. Joye, C.-E. Pfister : Exponentially small adiabatic invariant for the Schrödinger equation, Commun. Math. Phys. 140, p. 15-41 (1991). Zbl0755.35104MR92m:35058
  9. [JoPf2] A. Joye, C.-E. Pfister : Superadiabatic evolution and transition probability between two non-degenerate levels isolated in the spectrum, J. Math. Phys. 34 (1993), 454-479. Zbl0776.35056MR93m:81029
  10. [Ka] T. Kato : On the adiabatic theorem of quantum mechanics, J. Phys. Soc. J. Jpn. 5, 435-439 (1950). MR13,96g
  11. [Le] A. Lenard : Adiabatic invariants to all orders, Ann. Phys. 6, p. 261-276 (1959). Zbl0084.44403MR20 #7526
  12. [Ma1] A. Martinez : Estimates on Complex Interactions in Phase Space, Preprint Univ. Paris 13, Fev. 1992. 
  13. [Ma2] A. Martinez : Estimations sur l'effet tunnel microlocal, Séminaire E.D.P. de l'Ecole Polytechnique, 1991-1992. Zbl0778.35077
  14. [Ma3] A. Martinez : Precise exponential estimates in adiabatic theory, Preprint Univ. Paris 13, Avril 1993. Zbl0812.35108
  15. [Ne1] G. Nenciu : Adiabatic theorem and spectral concentration, Commun. Math. Phys. 82, p. 121-135, (1981). Zbl0493.47009MR83c:47025
  16. [Ne2] G. Nenciu : Linear Adiabatic Theory. Exponential Estimates, Commun. Math. Phys., to appear (1993). Zbl0768.34038MR95d:81018
  17. [Ne3] G. Nenciu : Exponential estimates in linear adiabatic theory : dependance on the gap, Preprint Mittag-Leffler Institute, 1993. Zbl0768.34038
  18. [Sa] S.J. Sancho : m-th order adiabatic invariance for quantum systems, Proc. Phys. Soc. Lond. 89, p. 1-5 (1966). Zbl0144.23501
  19. [Sj1] J. Sjöstrand : Singularités analytiques microlocales, Astérisque n° 95, 1982. Zbl0524.35007MR84m:58151
  20. [Sj2] J. Sjöstrand : Graduate Lecture at the University of Lund, 1985-1986 (Manuscript). 

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