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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
2010 Physical Review B  

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2010 pre-print arXiv:1011.4416v1 fatcat:itvzkxvyhnglznsd2ia2yedf6u
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 Φ(u,ϕ) we obtained an exact expression in quadratures for statistical moments I_q=〈 |ψ_E( r)|^2q〉 of normalized wavefunctions ψ_E( r) which show violation of one-parameter scaling and emergence of an additional length scale at E≈ 0.
doi:10.1103/physrevb.82.195120 fatcat:wz4bqyiuqbeqfhivzry53gdqqi
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V. E. Kravtsov, V. I. Yudson. "Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model." Physical Review B 82.19 (2010)