Bohm Aharonov effects for bounded states in the case of systems

O. Hebbar

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 4, page 489-500
  • ISSN: 0246-0211

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Hebbar, O.. "Bohm Aharonov effects for bounded states in the case of systems." Annales de l'I.H.P. Physique théorique 60.4 (1994): 489-500. <http://eudml.org/doc/76643>.

@article{Hebbar1994,
author = {Hebbar, O.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {comparison problem; eigenvalues; Laplacian; electric potential; vector bundle},
language = {eng},
number = {4},
pages = {489-500},
publisher = {Gauthier-Villars},
title = {Bohm Aharonov effects for bounded states in the case of systems},
url = {http://eudml.org/doc/76643},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Hebbar, O.
TI - Bohm Aharonov effects for bounded states in the case of systems
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 4
SP - 489
EP - 500
LA - eng
KW - comparison problem; eigenvalues; Laplacian; electric potential; vector bundle
UR - http://eudml.org/doc/76643
ER -

References

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  1. [1] J. Avron, I. Herbst and B. Simon, Schrödinger Operators with Magnetic Fields. I. General Interactions, Duke Math. Journal, 45, 1978, pp. 847-884. Zbl0399.35029MR518109
  2. [2] B. Doubrovine, S. Novikov and A. Fomenko, Géométrie contemporaine. Méthodes et applications, Éditions Mir, Moscou, 1979. Zbl0502.53002
  3. [3] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1977. Zbl0361.35003MR473443
  4. [4] O. Hebbar, Effet d'Aharonov-Bohm pour un état borné dans le cas des systèmes, Thèse de Doctorat à l'Université de Nantes (France), 1992. 
  5. [5] B. Helffer, Effet d'Aharonov-Bohm sur un état borné de l'équation de Schrödinger, Commun. Math. Phys., 119, 1988, 315-329. Zbl0702.35186MR968700
  6. [6] H. Hess, R. Schrader and D.A. Uhlenbrock, Domination of Semigroups and Generalization of Kato's Inequality, Duke Math. Journal, Vol. 44, 4, 1977. Zbl0379.47028
  7. [7] H. Hess, R. Schrader and D.A. Uhlenbrock, Kato's Inequality and the Spectral Distribution of Laplacian on Compact Riemannian Manifolds, J. Diff. Geometry, 15, 1980, pp. 27-37. Zbl0442.58032MR602436
  8. [8] R. Kuwabara, On Spectra of the Laplacian on Vector Bundles, J. Math. Tokushima Univ., 4, Vol. 16, 1982, pp. 1-23. Zbl0504.53039MR691445
  9. [9] R. Lavine and M. O'Caroll, Ground State Properties and Lower Bounds on Energy Levels of a Particle in a Uniform Magnetic Field and External Potential, J. Math. Phys., Vol. 18, 1977, pp. 1908-1912. MR456039
  10. [10] S. Manabe and I. Shigekawa, A Comparison Theorem for Eigenvalues of the Covariant Laplacian, J. Funct. Anal., Vol. 94, 1990, pp. 349-357. Zbl0716.58030MR1081648
  11. [11] M. Reed and B. Simon, Methods of modern mathematical physics, IV, New York, Academic press, 1978. Zbl0401.47001MR751959
  12. [12] I. Shigekawa, Eigenvalue Problems for the Schrödinger Operator with the Magnetic Field on a Compact Riemannian Manifold, J. Funct. Anal., 75, 1987, pp 92-127. Zbl0629.58023MR911202
  13. [13] R.O. Wells, Differential Analysis on Complex Manifolds, Grad. Texts. Math., Vol. 65, Springer-Verlag, 1979. Zbl0435.32004

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