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Anderson-like Transition for a Class of Random Sparse Models in d≥2 Dimensions

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Abstract

We show that the Kronecker sum of d≥2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

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Author notes

  1. Domingos H. U. Marchetti

    Present address: Mathematics Department, The University of British Columbia, Vancouver, BC, Canada, V6T 1Z2

Authors and Affiliations

  1. Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970, São Paulo, SP, Brazil

    Domingos H. U. Marchetti & Walter F. Wreszinski

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  1. Domingos H. U. Marchetti
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  2. Walter F. Wreszinski
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Correspondence to Domingos H. U. Marchetti.

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Marchetti, D.H.U., Wreszinski, W.F. Anderson-like Transition for a Class of Random Sparse Models in d≥2 Dimensions. J Stat Phys 146, 885–899 (2012). https://doi.org/10.1007/s10955-012-0439-4

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  • DOI: https://doi.org/10.1007/s10955-012-0439-4

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