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    • Absolutely Continuous Spectrum and Spectral Transition for some Continuous Random Operators

      M Krishna

      Volume 122 Issue 2 May 2012 pp 243-255

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/122/02/0243-0255

    • Keywords

       

      Random operators; a.c. spectrum.

    • Abstract

       

      In this paper we consider two classes of random Hamiltonians on $L^2(\mathbb{R}^d)$: one that imitates the lattice case and the other a Schrödinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for the Anderson model in higher dimension.

    • Author Affiliations

       

      M Krishna1

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

    • Dates

       
      Published
      May 2012
      Manuscript received
      28 February 2010
      Manuscript revised
      6 June 2011

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