This article is cited in 3 papers

Statistics of the Edge Green's Function for a One-Dimensional Disordered System with Binary or Uniform Diagonal Disorder

G. G. Kozlov

All-Russian Research Center "S. I. Vavilov State Optical Institute"

Abstract: For a one-dimensional diagonally disordered chain, we study the statistics of the edge Green's function (EGF) constructed using the random matrix of the Hamiltonian of this system. We assume that the disorder is either binary or uniform. We show that the EGF distribution function is not analytic in the case of binary disorder and propose a simple algorithm for constructing this function. We calculate the EGF distribution function exactly on some interval in the case of uniform disorder and propose a simple, effective method for determining this function completely and for calculating the mean EGF. We verify all the obtained results using direct computer diagonalization and observe a good agreement.

Keywords: disordered system, random matrix, Green's function, density of states.

Received: 21.07.2003
Revised: 16.10.2003

DOI: 10.4213/tmf90

 English version: Theoretical and Mathematical Physics, 2004, 140:2, 1175–1181

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