Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model

Details Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model

2010-11-19

arxiv.org/abs/1011.4416v1

Physical Review B, v.82, 195120 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 2 figures

Scientific paper

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 $I_{q}=\langle |\psi_{E}({\bf r})|^{2q}\rangle$ of normalized wavefunctions $\psi_{E}({\bf r})$ which show violation of one-parameter scaling and emergence of an additional length scale at $E\approx 0$.

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