Effet tunnel pour l'équation de Schrödinger avec champ magnétique

 Access to full text

 Full (PDF)

1. [AH - BO] Y. Aharonov - D. Bohm, Significance of Electromagnetic Potentials in the Quantum Theory. The Physical Review vol. 115 (3), Aug. 1959. Zbl0099.43102MR110458
2. [A - H - S] J. Avron - I. Herbst - B. Simon, Schrödinger Operators with Magnetic Fields. 
3. [1] General Interactions. Duke Math. J. vol.45 (4), Déc. 1978. 
4. [2] Separation of Center of Mass in Homogeneous Magnetic Fields. Ann. Physics114, pp. 431-451 (1978). Zbl0409.35027MR507741
5. [3] Atoms in Homogeneous Magnetic Fields. Comm. Math. Phys. 79 pp. 529-572 (1981). Zbl0464.35086MR623966
6. [C - S - S] J-M. Combes - R. Schrader - R. Seiler, Classical Bounds and Limits for Energy Distributions of Hamilton Operators in Electromagnetic Fields. Ann. Physics111, pp. 1-18 (1978). MR489509
7. [HE] B. Helffer, An introduction to Semi Classical Analysis for the Schrôdinger Operator. Cours en Chine. (A paraître Lecture Notes in Mathematics1988). 
8. [HE - RO] B. Helffer - D. Robert, Calcul Fonctionnel Admissible et Applications. J. Funct. Anal.53 (3) (1983), pp. 246-268. Zbl0524.35103MR724029
9. [HE - SJ] B. Helffer - J. Sjöstrand, Multiple Wells in the Semi-Classical Limit Zbl0546.35053
10. [1] Comm. in P.D.E., 9 (4) (1984), pp. 337-408. MR740094
11. [2] Interaction Moléculaire, Symétries, perturbation: Ann. Inst. H. Poincaré, vol. 42 (2) (1985), pp. 127-212. Zbl0595.35031MR798695
12. [HE - MA - RO] B. Helffer - A. Martinez - D. Robert, Ergodicité et Limite Semiclassique (Comm. Math. Phys.). Zbl0624.58039
13. [HO] L. Hörmander, The Analysis of Linear Partial Differential Equations. Tome 3, Chap. XXII - Springer. 
14. [HU] W. Hunziker, Schrôdinger Operators with Electric or Magnetic Fields. Proc. Int. Conf. in Math. Phys., Lausanne (1980). Zbl0471.47010MR582602
15. [IV] I.V. Ivrii - Note au C.R.A.S.1986, 302 Sér I (13), pp. 467-471. MR838401
16. [KA] T. Kato: [1] Israel J. Math.13 (1972) pp. 125-174. MR333833
17. [2] Perturbation Theory for Linear Operators. Grundlehren der Mathematischen Wissenschaften132. Springer Verlag. Zbl0531.47014
18. [ME - SJ] A. Menikoff - J. Sjöstrand.On the Eigenvalues of a class of hypoelliptic Operators. Math. Ann.235, pp. 55-85 (1978). Zbl0375.35014MR481627
19. [MO] A. Mohamed. 
20. [SI] B. Simon: [1] Indiana Univ. Math. J.26, pp. 1067-1073 (1977). Zbl0389.47021MR461209
21. [2] Semi-Classical Analysis of Low Lying Eingenvalues I. Ann. Inst. H. Poincaré t.38 (1983), pp. 295-307. 
22. [3] Semi-Classical Analysis of Low Lying Eingenvalues II. Tunneling. Ann. of Math. (1984) vol. 20, pp. 89-118. Zbl0626.35070
23. [SJ] J. Sjöstrand: [1] Singularités analytiques microlocales - Astérisque95 (1982). Zbl0524.35007MR699623
24. [2] Analytic Wave front Sets and Operators with Multiple CharacteristicsHokkaido Math. Journal Vol. XII (3), pp. 392-433. Zbl0531.35022
25. [WI] M. Wilkinson, Narrowly avoided crossings Preprint April 1986. 

1. Philippe Kerdelhué, Équation de Schrödinger en dimension 2, avec potentiel et champ magnétique périodiques. Cas d'un réseau triangulaire de puits
2. Gheorghe Nenciu, On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
3. B. Helffer, J. Sjöstrand, Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
4. Huirong Pi, Chunhua Wang, Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
5. Bernard Helffer, Bouteilles magnétiques et supraconductivité
6. Philippe Kerdelhué, Spectre de l'opérateur de Schrödinger magnétique avec symétrie d'ordre six
7. Philippe Kerdelhue, Équation de Schrödinger magnétique périodique avec symétrie d'ordre six : mesure du spectre II
8. Soeren Fournais, Bernard Helffer, Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian