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

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.