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    • Spectra of Anderson type models with decaying randomness

      M Krishna K B Sinha

      Volume 111 Issue 2 May 2001 pp 179-201

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/111/02/0179-0201

    • Keywords

       

      Anderson model; absolutely continuous spectrum; mobility edge; decaying randomness

    • 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.

    • Author Affiliations

       

      M Krishna1 2 K B Sinha1 2 3

      1. Institute of Mathematical Sciences, Taramani, Chennai - 600 113, India
      2. Indian Statistical Institute, 7 SJS Sansanwal Marg, New Delhi - 110 016, India
      3. Indian Statistical Institute, 203, BT Road, Kolkata - 700 035, India

    • Dates

       
      Published
      May 2001
      Manuscript received
      11 May 2000
      Manuscript revised
      17 November 2000

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