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Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian

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Abstract

We consider the Landau Hamiltonian (i.e. the 2D Schrödinger operator with constant magnetic field) perturbed by an electric potential V which decays sufficiently fast at infinity. The spectrum of the perturbed Hamiltonian consists of clusters of eigenvalues which accumulate to the Landau levels. Applying a suitable version of the anti-Wick quantization, we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity. We obtain an explicit description of the asymptotic density of the eigenvalues in terms of the Radon transform of the perturbation potential V.

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Authors and Affiliations

  1. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK

    Alexander Pushnitski

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna, 4860, Santiago de Chile, Chile

    Georgi Raikov

  3. Instituto de Matemáticas, Universidad Nacional Autonóma de México, Cuernavaca, Mexico

    Carlos Villegas-Blas

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  1. Alexander Pushnitski
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  2. Georgi Raikov
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  3. Carlos Villegas-Blas
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Correspondence to Alexander Pushnitski.

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Communicated by B. Simon

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Pushnitski, A., Raikov, G. & Villegas-Blas, C. Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian. Commun. Math. Phys. 320, 425–453 (2013). https://doi.org/10.1007/s00220-012-1643-4

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