Electron-electron interaction in disordered mesoscopic systems: Weak localization and mesoscopic fluctuations of polarizability and capacitance

The weak localization correction and the mesoscopic fluctuations of the polarizability and the capacitance of a small disordered sample are studied systematically in two-dimensional and three-dimensional geometries. While the grand canonical ensemble calculation gives the positive magnetopolarizability, in the canonical ensemble (appropriate for isolated samples) the sign of the effect is reversed. The magnitude of mesoscopic fluctuations for a single sample exceeds considerably the value of the weak localization correction.