Theoretical and Mathematical Physics

, Volume 179, Issue 1, pp 500–508 | Cite as

Calculation of the spectral dependence of the Anderson localization criterion in a one-dimensional system with correlated diagonal disorder

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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 

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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Fock Research Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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