Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder

Details Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder

1998-12-12

arxiv.org/abs/cond-mat/9812209v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages in RevTex and 2 Postscript figures; revised version published in Phys. Rev. Lett. 82 (1999) 4062

Scientific paper

10.1103/PhysRevLett.82.4062

We show that a mobility edge exists in 1D random potentials provided specific long-range correlations. Our approach is based on the relation between binary correlator of a site potential and the localization length. We give the algorithm to construct numerically potentials with mobility edge at any given energy inside allowed zone. Another natural way to generate such potentials is to use chaotic trajectories of non-linear maps. Our numerical calculations for few particular potentials demonstrate the presence of mobility edges in 1D geometry.

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