Periodic Schrödinger Operators with Constant Weak Magnetic Fields

B. Helffer; J. Sjöstrand

Recherche Coopérative sur Programme n°25 (1989)

  • Volume: 40, page 19-26

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Helffer, B., and Sjöstrand, J.. "Periodic Schrödinger Operators with Constant Weak Magnetic Fields." Recherche Coopérative sur Programme n°25 40 (1989): 19-26. <http://eudml.org/doc/274849>.

@article{Helffer1989,
author = {Helffer, B., Sjöstrand, J.},
journal = {Recherche Coopérative sur Programme n°25},
keywords = {magnetic fields; Peierls approximation},
language = {eng},
pages = {19-26},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Periodic Schrödinger Operators with Constant Weak Magnetic Fields},
url = {http://eudml.org/doc/274849},
volume = {40},
year = {1989},
}

TY - JOUR
AU - Helffer, B.
AU - Sjöstrand, J.
TI - Periodic Schrödinger Operators with Constant Weak Magnetic Fields
JO - Recherche Coopérative sur Programme n°25
PY - 1989
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 40
SP - 19
EP - 26
LA - eng
KW - magnetic fields; Peierls approximation
UR - http://eudml.org/doc/274849
ER -

References

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  5. [B2] J. Bellissard, C*-algebras in solid state physics, 2D-electrons in a uniform magnetic field, Warwick conference on operator algebras, July 1987. Zbl0677.46055MR996451
  6. [GuRT] J. C. Guillot, J. Ralston, E. Trubowitz, Semiclassical methods in solid state physics, Comm. Math. Physics, 116 (1988), 401-415 Zbl0672.35014MR937768
  7. [HS1] B. Helffer, J. Sjöstrand, Equation de Schrödinger avec champs magnétique et équation de Harper, Préprint (1988) 
  8. [HS2] B. Helffer, J. Sjöstrand, Opérateurs de Schrödinger avec champ magnétique faible, Sém. des E.D.P. de l'Ecole Polytéchnique, exp. n° . . . , 28 Fév. 1989. Zbl0634.35057
  9. [HS3] B. Helffer, J. Sjöstrand, In preparation. 
  10. [Hö] L. Hörmander, The analysis of linear partial differential operators III, Grundlehren der Math. Wiss., Springer, 274 (1985). Zbl0601.35001MR781536
  11. [L] J. M. Luttinger, The effect of a magnetic field on electrons in a periodic potentiel, Phys. Rev.84, n° 4 (1951), 814-817. Zbl0044.45301MR45052
  12. [N1] G. Nenciu, Existence of exponentially localized Wannier functions, Comm. Math. Phys., 91 (1983), 81-85. Zbl0545.47012MR719812
  13. [N2] G. Nenciu, Stability of energy gaps under variation of the magnetic field. Letters in Mathematical Physics, 11 (1986), 127-132. Zbl0607.46049MR836066
  14. [N3] G. Nenciu, Bloch electrons in a magnetic field: rigorous justification of the Peierls-Onsager effective Hamiltonian, preprint, (April 1988). Zbl0699.47007MR995804
  15. [P] R. Peierls, Zur Theorie des Diamagnetismus von Leitungelectronen, Z. für Physik80 (1933), 763-791. Zbl0006.19204JFM59.1576.09
  16. [Sh] Shubin, The density of states of selfadjoint elliptic operators with almost periodic coefficients. Trudy Sem. Petrovsk. n° 3 (1978), 243-275. Zbl0493.35041MR499819
  17. [Z] J. Zak, Magnetic translation group, Physical Review, Vol. 134, n° 6A, June 1964. Zbl0131.45404MR177769

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