Energy and current correlations in mesoscopic rings and quantum dots

With a view to some of the late developments in the thermodynamics of mesoscopic systems, we examine the problem of level correlations in moderately disorderd (diffusive) conductors. We briefly review the thermodynamic relations, employed within perturbation theory. We calculate correlation functions among single electron levels, and magnetic-field (magnetic-flux) derivatives thereof. Specifically, we evaluate both single-level current and single-level curvature correlations, and use them to examine the typical current, the paramagnetic susceptibility, and the energy ‘‘power spectrum’’ of Aharonov-Bohm geometries, derived previously. We stress the role of spectral rigidity, and present comparison with simply connected systems subject to a magnetic field.