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On the critical level-curvature distribution

S. N. Evangelou
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Abstract

The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a critical distribution which has the universal random matrix theory form ${\bar P}(K)\sim |K|^{-3}$ for large level-curvatures $|K|$ corresponding to quantum diffusion, although overall it is close to approximate log-normal statistics corresponding to localization. The obtained hybrid distribution resembles the critical distribution of the disordered Anderson model and makes a connection to recent experimental data.

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S. N. Evangelou. 2004-07-21. On the critical level-curvature distribution. https://doi.org/10.1088/1367-2630%2F6%2F1%2F200

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