Équilibre instable en régime semi-classique

Y. Colin de Verdière; B. Parisse

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-9

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Colin de Verdière, Y., and Parisse, B.. "Équilibre instable en régime semi-classique." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-9. <http://eudml.org/doc/112094>.

@article{ColindeVerdière1993-1994,
author = {Colin de Verdière, Y., Parisse, B.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {microlocal methods; eigenfunctions; dimension-one Schrödinger equation; Bohr-Sommerfeld conditions},
language = {fre},
pages = {1-9},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Équilibre instable en régime semi-classique},
url = {http://eudml.org/doc/112094},
year = {1993-1994},
}

TY - JOUR
AU - Colin de Verdière, Y.
AU - Parisse, B.
TI - Équilibre instable en régime semi-classique
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 9
LA - fre
KW - microlocal methods; eigenfunctions; dimension-one Schrödinger equation; Bohr-Sommerfeld conditions
UR - http://eudml.org/doc/112094
ER -

References

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  1. [1] R. Brummelhuis, T. Paul, and A. Uribe.Spectral estimates around a critical level. Manuscrit, Reims, 1993. Zbl0849.58067
  2. [2] J. Carry and P. Rusu.Separatrix eigenfunction. Physical Review A, 45(12):8501-8512, 15 June 1992. 
  3. [3] Y. Colin de Verdière and B. Parisse.Équilibre instable en régime semi-classique - I. Concentration microlocale. Prépublication de d'Institut Fourier, 252, 1993. Zbl0819.35116MR1294470
  4. [4] Y. Colin de Verdière and B. Parisse.Équilibre instable en régime semi-classique - II. Conditions de Bohr-Sommerfeld. En préparation, 1994. Zbl0845.35076MR1311072
  5. [5] Y. Colin de Verdière and J. Vey.Le lemme de Morse isochore. Topology, 18:283-299, 1979. Zbl0441.58003MR551010
  6. [6] P. Duclos and H. Hogreve.On the semi-classical localization of quantum probability. J. Math. Phys., 34(5):1681-1691, 1993. Zbl0773.60094MR1214482
  7. [7] J. Duistermaat.Oscillatory integrals, lagrange immersions and unfolding of singularities. C.P.A.M., 27:207-281, 1974. Zbl0285.35010MR405513
  8. [8] K. Ford, D. Hill, M. Wakeno, and J. Wheeler.Quantum Effects near a Barrier Maximum. Annals of Physics, 7:239-258, 1959. Zbl0086.22406MR104479
  9. [9] C. Gérard and A. Grigis.Precise estimates of tunneling and eigenvalues near a potential barrier. Journal of Differential Equations, 72:149-177, 1988. Zbl0668.34022MR929202
  10. [10] P. Gérard.Microlocal defect measures. Comm. PDE, 16(11):1761-1794, 1991. Zbl0770.35001MR1135919
  11. [11] B. Helffer, A. Martinez, and D. Robert.Ergodicité et limite semi-classique. Communications in Mathematical Physics, 109:313-326,1987. Zbl0624.58039MR880418
  12. [12] B. Helffer and J. Sjöstrand.Multiple wells in the semi-classical limit-I. Communication in Partial Differential Equation, 9(4):337-408, 1984. Zbl0546.35053MR740094
  13. [13] B. Helffer and J. Sjöstrand.Semi-classical analysis for Harper's equation- III. Cantor structure of the spectrum. Bulletin de la Société Mathématique de France, 117(4), 1989. Zbl0725.34099MR832011
  14. [14] W. Horn.Semiclassical approximations for tunneling near the top of a potential barrier and its applications to solid state physics. PhD thesis, UCLA, 1989. 
  15. [15] C. März.Spectral Asymptotics for Hill's Equation near the potential maximum. Asymptotic Analysis, 5:221-267, 1992. Zbl0786.34080MR1145112
  16. [16] J. Sjöstrand.Density of state oscillations for magnetic Schrödinger operator. In Bennewitz, editor, Differential Equations and Mathematical Physics, pages 295-345, University of Alabama at Birmingham, March 15-21 1990. Zbl0778.35089MR1126702
  17. [17] L. Tartar.H-measures, a new approach for studying homogenization oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh, 115A:193-230, 1990. Zbl0774.35008MR1069518

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