Analyse semi-classique pour l'équation de Harper

B. Helffer; J. Sjöstrand

Séminaire Équations aux dérivées partielles (Polytechnique) (1986-1987)

  • page 1-12

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Helffer, B., and Sjöstrand, J.. "Analyse semi-classique pour l'équation de Harper." Séminaire Équations aux dérivées partielles (Polytechnique) (1986-1987): 1-12. <http://eudml.org/doc/111915>.

@article{Helffer1986-1987,
author = {Helffer, B., Sjöstrand, J.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {spectrum; Harper's equations; semi-classical analysis},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Analyse semi-classique pour l'équation de Harper},
url = {http://eudml.org/doc/111915},
year = {1986-1987},
}

TY - JOUR
AU - Helffer, B.
AU - Sjöstrand, J.
TI - Analyse semi-classique pour l'équation de Harper
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1986-1987
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - spectrum; Harper's equations; semi-classical analysis
UR - http://eudml.org/doc/111915
ER -

References

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  1. I.S. Aubry, C. André, Proc.Israel Phys.Soc.,ed.C.G.Kuper 3(Adam Hilger, Bristol, 1979), 133-. 
  2. 2 M. Ya. Az bel, Energy spectrum or a conduction electron in a magnetic field, Zh. Eksp. Teor. Fiz.46,(1964),939-, Sov. Phys. JETP19,(1964),634-. 
  3. 3 J. Bellisard, B., Simon, Cantor spectrum for the almost Mathieu equation, J. Funct.Anal.,48(3),408-419. Zbl0516.47018MR678179
  4. 4 U. Carlsson, Travail en préparation. 
  5. 5 B. Helffer,D,Robert, Puits de potentiel généralisés et asymptotique semi-classique, Ann. de l'IHP,41(3)(1984),291-331. Zbl0565.35082MR776281
  6. 6 B. Helffer, J., Sjöstrand, Multiple wells in the semi-classical limit I. Comm. in PDE, 9(4)(1984),337-408. Zbl0546.35053MR740094
  7. 7 B. Helffer, J. Sjöstrand, Puits mulptiples.,II,Intéraction moléculaire, symétries, perturbation. Ann. de l'IHP,42(2)(1985),127-212. Zbl0595.35031MR798695
  8. 8 B. Helffer, J. Sjöstrand, Effet tunnel pour l'équation de Schrôdinger avec champ magnétique. Préprint de l'Ecole Polytechnique,Déc.1986. Zbl0699.35205
  9. 9 D.R. Hofstadter,Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B, 14(6), 15Sept. 1976. 
  10. 10 B. Simon, Almost periodic Schrödinger operators. A review, Adv.Appl.Math. 3,(1982),463-490. Zbl0545.34023MR682631
  11. 11 J. Sokoloff, Unusual band structure, wave functions and electrical conductance in crystals with incommensurate periodic potentials, Physics reports (Review section of Physics letters), 126(4)(1985), 189-244. 
  12. 12 M. Wilkinson, Critical properties of electron eigenstates in incommensurate systems, Proc.R.Soc.Lond., A391,(1984),305-350. MR739684
  13. 13 M. Wilkinson, An example of phase holonomy in WKB theory, J. Phys. A, 17(1984),3459-3476. MR772333
  14. 14 M. Wilkinson, Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field, Proc. R. Soc. Lond., A403,(1986),135-166. MR828687
  15. 15 M. Wilkinson, An exact renormalisation group for Bloch electrons in a magnetic field, J. Phys. A., à paraître. 

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