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Density of states of random Schrödinger operators with a uniform magnetic field

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Abstract

We consider the density of states of Schrödinger operators with a uniform magnetic field and a random potential with a Gaussian distribution. We show that the restriction to the states of the first Landau level is equivalent to a scaling limit where one looks at the density of states near to the energy of the first Landau level and simultaneously lets the strength of the coupling to the random potential go to zero. We also consider a different limit where we look at the suitably normalised density of states near to the energy of the first Landau level when the intensity of the magnetic field goes to infinity.

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References

  1. Wegner, F., Z. Phys. B51, 279 (1983).

    Google Scholar 

  2. Itzykson, C. and Zuber, J. B., Quantum Field Theory, McGraw-Hill, New York, 1980.

    Google Scholar 

  3. Smith, C. A. B. and Tutte, W. T., Amer. Math. Monthly 48, 233 (1941); Smith, C. A. B., Tutte, W. T., and Kasteleyn, P. W., in F. Harary (ed), Graph Theory and Theoretical Physics, Academic Press, New York, 1967, p. 44.

    Google Scholar 

  4. Brezin, E., Gross, D. J., and Itzykson, C., Nuclear Phys. B235 [FS11], 24 (1984).

    Google Scholar 

  5. Klein, A. and Perez, J. F., Nuclear Phys. B25 [FS13], 199 (1985).

    Google Scholar 

  6. Lloyd, P., J. Phys. C2, 1717 (1969).

    Google Scholar 

  7. Kunz, H. and Zumbach, G., Nuclear Phys. B270 [FS16], 347 (1986).

    Google Scholar 

  8. Simon, B., Functional Integration and Quantum Physics, Academic Press, New York, 1979.

    Google Scholar 

  9. MacAonghusa, P. and Pule, J. V., Stochastics Stochastics Rep. 26, 247 (1989).

    Google Scholar 

  10. Macris, N., PhD Thesis, Equilibre de ionisation en mécanique statistique, Ecole Polytechnique Federale de Lausanne, 1990.

  11. Bourbaki, N., Elements de Mathematiques, Chap IX Integration, Hermann, Paris, 1969.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Physics, Rutgers University, 08903, New Brunswick, NJ, USA

    N. Macris

  2. Department of Mathematical Physics, University College Belfield, Dublin 4, Ireland

    J. V. Pule

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  1. N. Macris
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  2. J. V. Pule
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Macris, N., Pule, J.V. Density of states of random Schrödinger operators with a uniform magnetic field. Lett Math Phys 24, 307–321 (1992). https://doi.org/10.1007/BF00420490

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  • DOI: https://doi.org/10.1007/BF00420490

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