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

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.

4 pages (revtex), 1 figure (ps file)

References in corpus (3)

• Level Curvatures and Conductances: A Numerical Study of the Thouless Relation
• Distribution of level curvatures for the Anderson model at the localization-delocalization transition
• Non-universal corrections to the level curvature distribution beyond random matrix theory

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