Advertisement

On the Quantum Hall-Effect

  • Ruedi Seiler
Chapter
Part of the Mathematical Physics Studies book series (MPST, volume 12)

Abstract

In these lectures I will try to give you an impression about the Quantum Hall-Effect. The theoretical point of view will mainly be the one developed by Y. Avron and myself [1,2,3]. The section on corrections to the Kubo formula is based on some work together with M. Klein [4]. During the three hours of these lectures it will be impossible to do justice to all authors who have contributed to this field.

Keywords

Vector Bundle Chern Class Selfadjoint Operator Quantum Hall Effect Hall Current 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Avron, J.E., Seiler, R.: Quantisation of the Hall conductance for general multiparticle Schrödinger Hamiltonians.Phys. Rev. Lett. 54, 259–262 (1985).MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    Avron, J.E., Seiler, R., Yaffe, L.G.: Adiabatic Theorems and Applications to the Quantum Hall Effect. Commun. Math. Phys. 110, 33–49 (1987).MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. [3]
    Avron, Y., Seiler, R., Shapiro, B.: General Properties of Quantum Hall Hamiltonians for Finite Systems. Nucl. Phys. B 265, 364–374 (1986).MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    Klein, M., Seiler, R.: Power-law Corrections to the Kubo Formula Vanish in Quantum Hall Systems. Technische Universität Berlin, Fachbereich Mathematik MA 7–2, D1000 Berlin 12, Reprint 214 (1989).Google Scholar
  5. [5]
    von-Klitzing, K., Dorda, G., Pepper, M.: New method for high accuracy determination of the fine structure constant based on the quantized Hall effect. Phys. Rev. Lett. 45, 494–497 (1980).ADSCrossRefGoogle Scholar
  6. [6]
    Laughlin, R.B.: Phys. Rev. Lett. 50, 1395–1398 (1983).Phys. Rev. B 27, 3383–3389 (1983).Google Scholar
  7. [7]
    Laughlin, R.B.: Quantized Hall Conductivity in Two Dimensions. Phys. Rev. B 23, 5652–5654 (1981).ADSCrossRefGoogle Scholar
  8. [8]
    Thouless, D.J., Kohmoto, M., Nightingale, M., den-Nys, M.: Quantized Hall Conductance in a two dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).ADSCrossRefGoogle Scholar
  9. [9]
    Dubrovin B.A., Novikov S.P.: Ground states of two-dimensional electron in a periodic magnetic field. Sov.Phys.JETP 52, 511–516 (1980)MathSciNetADSGoogle Scholar
  10. [10]
    Novikov S.P.: Magnetic Bloch functions and vector bundles. Sov. Math. Dokl. 23, 298–303 (1981)zbMATHGoogle Scholar
  11. [11]
    Niu, Q., Thouless, D.J.: Quantized adiabatic charge transport in the presence of substrate disorder and many body interactions. J. Phys. A 9, 30–49 (1984).MathSciNetGoogle Scholar
  12. [12]
    Avron, J.E., Seiler, R., Simon, B.: Homotopy and Quantization in Condensed Matter Physics. Phys. Rev. Lett. 51, 51–53 (1983).ADSCrossRefGoogle Scholar
  13. [13]
    Nenciu, G.: Adiabatic Theorem and Spectral Concentration. Commun. Math. Phys. 82, 121–135 (1981).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. [14]
    Prange, R.E., Girvin, S.M. (Editors): The Quantum Hall Effect. Graduate Texts in Contemporary Physics, Springer-Verlag (1987).Google Scholar
  15. [15]
    Bellissard, J.: C-Algebras in Solid State Physics. 2D Electrons in a uniform magnetic field. Operator Algebras and Applications, Vol. 2. D.E. Evans and M. Takesaki Eds., London Math. Soc. Lecture Notes 136, Cambridge (1988).Google Scholar
  16. [16]
    Kato, T.: On the Adiabatic Theorem of Quantum Mechanics. J. Phys. Soc. Jap. 5, 435–439 (1950).ADSCrossRefGoogle Scholar
  17. [17]
    Berry, M.: Quantal Phase Factors Accompagnying Adiabatic Changes. Proc. Roy. Soc. London A 392, 45–57 (1984).ADSzbMATHCrossRefGoogle Scholar
  18. [18]
    Simon, B.: Holonomy, the Quantum Adiabatic Theorem and Berry’s Phase. Phys. Rev. Lett. 51, 2167–290 (1983).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Ruedi Seiler
    • 1
  1. 1.Technische Universität Berlin MA7-2Berlin 12Germany

Personalised recommendations