Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model
Abstract
An exact solution is found for the problem of the center-of-band (E=0) anomaly in the one-dimensional 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 Iq=⟨|ψE(r)|2q⟩ of normalized wave functions ψE(r) which show violation of one-parameter scaling and emergence of an additional length scale at E≈0 .
- Publication:
-
Physical Review B
- Pub Date:
- November 2010
- DOI:
- 10.1103/PhysRevB.82.195120
- arXiv:
- arXiv:1011.4416
- Bibcode:
- 2010PhRvB..82s5120K
- Keywords:
-
- 72.15.Rn;
- 72.20.Ht;
- 72.70.+m;
- 73.23.-b;
- Localization effects;
- High-field and nonlinear effects;
- Noise processes and phenomena;
- Electronic transport in mesoscopic systems;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 5 pages, 2 figures