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Splitting Landau Levels On The 2d Torus By Periodic Perturbations

Author

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  • E. ONOFRI

    (Laboratoire de Physique Théorique et Astroparticules, Université Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 05, France)

Abstract

We study the spectrum of the Schroedinger operator for a particle constrained on a two-dimensional flat torus under the combined action of a transverse magnetic field and a conservative force. A numerical method is presented which allows to compute the spectrum with high accuracy. The method employs a fast Fourier transform to accurately represent the momentum variables and takes into account the twisted boundary conditions required by the presence of the magnetic field. An accuracy of 12 digits is attained even with coarse grids. Landau levels are reproduced in the case of a uniform magnetic field satisfying Dirac's condition. A new fine structure of levels within the single Landau level is formed when the field has a sinusoidal component with period commensurable to the integer magnetic charge. This fact is interpreted in terms of the peculiar symmetryZN× ZNwhich holds in the unperturbed case.

Suggested Citation

  • E. Onofri, 2008. "Splitting Landau Levels On The 2d Torus By Periodic Perturbations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(11), pages 1753-1761.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:11:n:s0129183108013266
    DOI: 10.1142/S0129183108013266
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