• Random matrix model for disordered conductors

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      https://www.ias.ac.in/article/fulltext/pram/054/03/0413-0422

    • Keywords

       

      Disordered conductors; random matrix theory; Dyson’s Coulomb gas model

    • Abstract

       

      We present a random matrix ensemble where real, positive semi-definite matrix elements, x, are log-normal distributed, exp[−log2(x)]. We show that the level density varies with energy, E, as 2/(1+E) for large E, in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson’s Coulomb gas analogy breaks down whenever the confining potential is given by a transcendental function for which there exist orthogonal polynomials.

    • Author Affiliations

       

      Zafar Ahmed1 Sudhir R Jain1 2

      1. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai - 400 085, India
      2. Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai - 400 085, India
    • Dates

       
  • Pramana – Journal of Physics | News

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