Effet tunnel pour des puits sous-variétés

B. Helffer

Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986)

  • page 1-14

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Helffer, B.. "Effet tunnel pour des puits sous-variétés." Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986): 1-14. <http://eudml.org/doc/111885>.

@article{Helffer1985-1986,
author = {Helffer, B.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Schrödinger operator; smooth Riemannian manifold; semi classical limit; ground state; non-degenerate wells; Agmon distance; Dirichlet boundary conditions; BKW methods; continuous symmetries; Morse inequalities; method of Witten},
language = {fre},
pages = {1-14},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Effet tunnel pour des puits sous-variétés},
url = {http://eudml.org/doc/111885},
year = {1985-1986},
}

TY - JOUR
AU - Helffer, B.
TI - Effet tunnel pour des puits sous-variétés
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1985-1986
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 14
LA - fre
KW - Schrödinger operator; smooth Riemannian manifold; semi classical limit; ground state; non-degenerate wells; Agmon distance; Dirichlet boundary conditions; BKW methods; continuous symmetries; Morse inequalities; method of Witten
UR - http://eudml.org/doc/111885
ER -

References

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  1. [AB-MA] Abraham-Marsden, Foundations of Mechanics Zbl0158.42901
  2. [B1] J.M. Bismut, The Witten complex and the degenerate Morse inequalitiesPreprint de l'Université d'Orsay 84 T 41. Zbl0608.58038MR852155
  3. [BO] R. Bott, Non degenerate critical manifolds;Ann. of Math.60, p.248-2611954. Zbl0058.09101MR64399
  4. [HE] B. Helffer, An introduction to the semi-classical analysis for on the Schrödinger operator - cours en Chine- 
  5. [HE-RO] B. Helffer, D. Robert, Puits de potentiels généralisés et asymptotique semi-classique;Annales de l'I.H.P. (Section Physique théorique) vol.42 n°2, 1985 p.127-212. MR798695
  6. [HE-SJ] B. Helffer, J. Sjöstrand [1] Multiple wells in the semi-classical limit I;(comm. in P.D.E., 9 (4), p.337-408 (1984). Zbl0546.35053MR740094
  7. [2] Puits multiples en limite semi-classique II Interaction moléculaire. Symétries - perturbations;Annales de l'I.H.P. (Section Physique théorique) vol.42, n°2, 1985 p.127-212. Zbl0595.35031MR798695
  8. [3] Multiple wells in the semi-classical limit III Non resonant Wells; Math. Nachr.124 (1985) p.263-313. Zbl0597.35023MR827902
  9. [4] Puits multiples en limite semi-classique IV Etude du complexe de Witten; comm. in P.D.E., 10 (3) p245-340 (1985). Zbl0597.35024
  10. [5] Puits multiples en mécanique semi-classique V:étude des minipuits (à paraître). 
  11. [6] Puits multiples en mécanique semiclassique VI:cas des puits uniformément dégénérés (en préparation) 
  12. [7] Conférences à St Jean de Monts; Actes du colloque de St Jean de Monts Juin 1985. Publications de l'Ecole Polytechnique 
  13. [HO] L. Hörmander, The Cauchy problem for differential equations with double caracteristics. J. Analyse Math.32, 1977 p.118-196. Zbl0367.35054MR492751
  14. [ME] A. Melin, Lower bounds for pseudodifferential operators;Ark. för Mat.9 (1971), p.117-140. Zbl0211.17102MR328393
  15. [SI] B. Simon [1] Semi-classical analysis of low lying eigenvalues;Non degenerate minima: Asymptotics expansions; Ann. Inst. H. Poincaré38 (1983) p.295-307. Zbl0526.35027MR708966
  16. [2] Semi-classical of low lying eigenvalues II. TunnelingAnnals of Math. (1984). Zbl0626.35070
  17. [3] Communication personnelle (Mars 1984). 
  18. [WI] E. Witten, super symmetry and Morse theoryJ. of differential geometry17 (1982) p.661-692. Zbl0499.53056MR683171
  19. [CDS] J.M. Combes, P. Duclos, R. Seiler (1983) convergent expansions for TunnelingComm. Math. Phys.92, p.229-245. Zbl0579.47050MR728868
  20. [CO] S. Coleman, "The Use of Instantons" Proceedings of the 1977 International School of Subnuclear Physics, A. Zichichi Editor, pp 805-916, PlenumNew-York1979. 
  21. [HA] E.M. Harrel, "Double Wells" [1980]Comm. Math. Phys.75, p.239-261. Zbl0445.35036MR581948

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