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Spectra of Anderson type models with decaying randomness

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Abstract

In this paper we consider some Anderson type models, with free parts having long range tails and with the random perturbations decaying at different rates in different directions and prove that there is a.c. spectrum in the model which is pure. In addition, we show that there is pure point spectrum outside some interval. Our models include potentials decaying in all directions in which case absence of singular continuous spectrum is also shown.

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Author notes

  1. K. B. Sinha

    Present address: Indian Statistical Institute, 203, BT Road, 700 035, Kolkata, India

Authors and Affiliations

  1. Institute of Mathematical Sciences, Taramani, 600 113, Chennai, India

    M. Krishna & K. B. Sinha

  2. Indian Statistical Institute, 7 SJS Sansanwal Marg, 110 016, New Delhi, India

    M. Krishna & K. B. Sinha

Authors
  1. M. Krishna
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  2. K. B. Sinha
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Correspondence to M. Krishna.

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Krishna, M., Sinha, K.B. Spectra of Anderson type models with decaying randomness. Proc. Indian Acad. Sci. (Math. Sci.) 111, 179–201 (2001). https://doi.org/10.1007/BF02829590

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  • DOI: https://doi.org/10.1007/BF02829590

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