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A new method of calculation in the Fractional Quantum Hall Effect regime

  • Research Article
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Central European Journal of Physics

Abstract

The electron-electron and electron-background interaction energies are calculated analytically for systems with up to N = 6 electrons. The method consists of describing the position vectors of electrons using complex coordinates and all the interaction energies with complex notation, whereby simplifications become possible. As is known, in this type of calculation, complicated expressions involving integrals over many variables are encountered and the trick of using complex coordinates greatly facilitates the exact calculation of various quantities. Contrary to previous analytical calculations, using complex coordinates avoids complicated trigonometric functions from appearing in the integrand, simplifying the exact evaluation of the integrals. The method we have used can be straightforwardly extended to larger systems with N > 6 electrons.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Université de Tlemcen, B.P. 230, 13000, Tlemcen, Algeria

    Zine el abidine Bentalha, Larabi Moumen & Tarik Ouahrani

  2. département de Physique, École Préparatoire Sciences et Techniques, B.P. 230, 13000, Tlemcen, Algeria

    Tarik Ouahrani

Authors
  1. Zine el abidine Bentalha
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  2. Larabi Moumen
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  3. Tarik Ouahrani
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Correspondence to Zine el abidine Bentalha.

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Bentalha, Z.e.a., Moumen, L. & Ouahrani, T. A new method of calculation in the Fractional Quantum Hall Effect regime. centr.eur.j.phys. 12, 511–516 (2014). https://doi.org/10.2478/s11534-014-0476-5

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  • DOI: https://doi.org/10.2478/s11534-014-0476-5

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