On an example of phase-space tunneling

Shu Nakamura

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 63, Issue: 2, page 211-229
  • ISSN: 0246-0211

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Nakamura, Shu. "On an example of phase-space tunneling." Annales de l'I.H.P. Physique théorique 63.2 (1995): 211-229. <http://eudml.org/doc/76693>.

@article{Nakamura1995,
author = {Nakamura, Shu},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {phase space tunneling; Born-Oppenheimer approximation; resonance},
language = {eng},
number = {2},
pages = {211-229},
publisher = {Gauthier-Villars},
title = {On an example of phase-space tunneling},
url = {http://eudml.org/doc/76693},
volume = {63},
year = {1995},
}

TY - JOUR
AU - Nakamura, Shu
TI - On an example of phase-space tunneling
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 63
IS - 2
SP - 211
EP - 229
LA - eng
KW - phase space tunneling; Born-Oppenheimer approximation; resonance
UR - http://eudml.org/doc/76693
ER -

References

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  1. [1] J. Asch and P. Duclos, An elementary model of dynamical tunneling, in Differential Equations with Applications to Mathematical Physics (F. AMES, J. V., HEROD, E. HARREL eds.), Academic Press, 1993, pp. 1-11. Zbl0789.35127MR1207143
  2. [2] D. Babbit and E. Balslev, Local distortion technique and unitarity of the S-matrix for the 2-body problem, J. Math. Anal. Appl., Vol. 54, 1976, pp. 316-347. MR413860
  3. [3] J.M. Combes, P. Duclos, M. Klein and R. Seiler, The shape resonance, Commun. Math. Phys., Vol. 110, 1987, pp. 215-236. Zbl0629.47044MR887996
  4. [4] H.L. Cycon, R.G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry, Springer Verlag, Berlin, 1987. Zbl0619.47005MR883643
  5. [5] G.B. Folland, Harmonic Analysis in Phase Space, Princeton Univ, Press, Princeton, 1989. Zbl0682.43001MR983366
  6. [6] B. Helffer and J. Sjöstrand, Multiple wells in the semiclassical limit, I., Comm. P.D.E., Vol. 9, 1984, pp. 337-408. Zbl0546.35053MR740094
  7. [7] B. Helffer and J. Sjöstrand, Résonances en limite semi-classique, Mem. Soc. Math., France, Vol. 24/25, 1986, pp. 1-228. Zbl0631.35075MR871788
  8. [8] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Springer Verlag, Berlin, 1985. Zbl0601.35001MR404822
  9. [9] W. Hunziker, Distortion analyticity and molecular resonance curbes, Ann. Inst. H. Poincaré, Vol. 45, 1986, pp. 339-358. Zbl0619.46068MR880742
  10. [10] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer Verlag, Berlin, 1976, Zbl0342.47009MR407617
  11. [11] M. Klein, A. Martinez, R. Seiler and X.P. Wang, On the Born-Oppenbeiraer expansion for polyatomic molecules, Commun. Math. Phys., Vol. 143, 1992, pp. 607-639. Zbl0754.35099MR1145603
  12. [12] A. Martinez, Estimates on complex interactions in phase space, preprint 1992, Université Paris-Nord (To appear in Mathematische Nachrichten). MR1226487
  13. [13] A. Martinez, Precise exponential estimates in adiabatic theory, preprint 1993, Université Paris-Nord (To appear in J. Math. Phys.). MR1240530
  14. [14] A. Martinez, Résonances dans l'approximation de Born-Oppenheimer, I., J. Diff. Eq., Vol. 91, 1991, pp. 204-234; II. Commun, Math. Phys., Vol. 135, 1991, pp. 517-530. Zbl0737.35046MR1091576
  15. [15] S. Nakamura, Tunneling estimates in momentum space and scattering, preprint 1993, University of Tokyo (To appear in Spectral and Scattering Theory (ed. M. IKAWA), Marcel Decker, New York, 1994). 
  16. [16] S. Nakamura, On Martinez' method of phase space tunneling, preprint, 1994, University of Tokyo (To appear in Rev. Math. Phys.). MR1326141
  17. [17] B. Simon, Semiclassical analysis of low-lying eigenvalues, II. Tunneling, Ann. Math., Vol. 120, 1984, pp. 89-118. Zbl0626.35070MR750717

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