publication . Preprint . Article . 2005

Level statistics of Anderson model of disordered systems: connection to Brownian ensembles

Pragya Shukla;
Open Access English
  • Published: 26 Feb 2005
Abstract
Comment: 19 Pages, 10 Figures, Published Version
Subjects
free text keywords: Condensed Matter - Statistical Mechanics, General Materials Science, Condensed Matter Physics, Statistics, Anderson impurity model, Statistical physics, Metal–insulator transition, Brownian motion, Critical point (mathematics), Scaling, Parametric statistics, Gaussian, symbols.namesake, symbols, Physics, Critical point (thermodynamics)
38 references, page 1 of 3

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[11] The higher order correlations basically being the measures of the fluctuations of the density around its average value, their comparison in two different spectrum makes sense only if the fluctuations are measured with respect to same background. This requires an unfolding of each spectrum, that is, rescaling by its mean level density before comparison with another spectrum [4]. As the parameter governing the evolution in the rescaled spectrum is Λ, the higher order correlations of an AE are given by a BE with a same Λ value.

[12] For a d dimensional disordered system, the number of states in a volume of linear dimension ζ in d-dimensions is n(0)ζd, with n(0) as the density of states at Fermi level and ζ as the localization length. Consequently, the typical energy separation between such states is Δl(E, Y ) = (n(0)ζd)−1. Similarly the mean level spacing of states in the full length of the spectrum is Δ(E, Y ) = (n(0)Ld)−1 which gives R1 = Δ−1 = n(0)Ld. For disordered systems, Δl can therefore be expressed in terms of the mean level density R1: Δl = (L/ζ)dR1−1.

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[15] B.Kramer and A. MacKinnon, Rep. Prog. Phys. 56, (1469) (1993).

38 references, page 1 of 3
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publication . Preprint . Article . 2005

Level statistics of Anderson model of disordered systems: connection to Brownian ensembles

Pragya Shukla;