"Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results

TL;DR

This paper analytically derives the distribution of level curvatures in diffusive Aharonov-Bohm systems, confirming the Zakrzewski-Delande conjecture and establishing a universal ratio between mean level curvature and conductance.

Contribution

It provides an analytical calculation of level curvature distributions and verifies the universality of their ratio to conductance in diffusive quantum systems.

Findings

Zakrzewski-Delande conjecture remains valid with weak localization corrections

Universal ratio of mean level curvature modulus to dissipative conductance is 2π

Analytical results agree with numerical data

Abstract

We calculate analytically the distributions of "level curvatures" (LC) (the second derivatives of eigenvalues with respect to a magnetic flux) for a particle moving in a white-noise random potential. We find that the Zakrzewski-Delande conjecture is still valid even if the lowest weak localization corrections are taken into account. The ratio of mean level curvature modulus to mean dissipative conductance is proved to be universal and equal to $2\pi$ in agreement with available numerical data.