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Log-normal Distribution of Level Curvatures in the Localized Regime: Analytical Verification

Michael Titov·Daniel Braun·Yan V. Fyodorov
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Abstract

We study numerically and analytically the moments of the dimensionless level curvature for one-dimensional disordered rings of the circumference L pierced by a magnetic flux. The negative moments of the curvature distribution can be evaluated analytically in the extreme localization limit. The ensuing small curvature asymptotic of the corresponding distribution has a "log-normal" behavior. Numerically studied positive moments show differences from other log-normally distributed quantities.

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Michael Titov, Daniel Braun, Yan V. Fyodorov. 1996-11-28. Log-normal Distribution of Level Curvatures in the Localized Regime: Analytical Verification. https://doi.org/10.1088/0305-4470%2F30%2F10%2F007

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