Calculation of spectral dependence of Anderson criterion for 1D system with correlated diagonal disorder

G. G. Kozlov

Fock Research Institute of Physics, St. Petersburg State University, St. Petersburg, Russia

Abstract: We consider the problem of calculating the Anderson criterion for a one-dimensional disordered chain with correlated disorder. We solve this problem by the perturbation method with the inverse correlation length as the small parameter. We show that in a correlated system, the degree of localization not only naturally decreases but its spectral dependence also differs significantly from the spectral dependence in uncorrelated chains. The calculations are based on the method for constructing joint statistics of Green's functions, which was previously used to analyze uncorrelated one-dimensional systems. We illustrate the theoretical calculations with a numerical experiment.

Keywords: Anderson localization, correlated disorder, Green's function.

Received: 23.09.2013

DOI: 10.4213/tmf8598

 English version: Theoretical and Mathematical Physics, 2014, 179:1, 500–508

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