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26 April 2024

» arxiv » 1011.4416

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Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model
V.E.Kravtsov ; V.I.Yudson ;
Date:	19 Nov 2010
Abstract:	An exact solution is found for the problem of the center-of-band ($E=0$) anomaly in the one-dimensional (1D) Anderson model of localization. By deriving and solving an equation for the generating function $Phi(u,phi)$ we obtained an exact expression in quadratures for statistical moments $I_{q}=langle \|psi_{E}({f r})\|^{2q} angle$ of normalized wavefunctions $psi_{E}({f r})$ which show violation of one-parameter scaling and emergence of an additional length scale at $Eapprox 0$.
Source:	arXiv, 1011.4416
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