Magnetic susceptibility of disordered nondiffusive mesoscopic systems

Disorder-induced spectral correlations of mesoscopic quantum systems in the nondiffusive regime, and their effect on the magnetic susceptibility, are studied. We perform impurity averaging for nontranslational invariant systems by combining a diagrammatic perturbative approach with semiclassical techniques. This allows us to study the entire range from clean to diffusive systems. As an application we consider the magnetic response of noninteracting electrons in microstructures in the presence of weak disorder. We show that in the ballistic case (an elastic mean free path l larger than the system size) there exist two distinct regimes of behavior depending on the relative magnitudes of l and an inelastic scattering length $L_{\phi }.$ We present numerical results for square billiards, and derive approximate analytical results for generic chaotic geometries. The magnetic-field dependence and the $L_{\phi }$ dependence of the disorder-induced susceptibility are qualitatively similar in both types of geometry.