  We examine oscillations as a function of Fermi energy in the capacitance of a
mesoscopic cavity connected via a single quantum channel to a metallic contact
and capacitively coupled to a back gate. The oscillations depend on the
distribution of single levels in the cavity, the interaction strength and the
transmission probability through the quantum channel. We use a Hartree-Fock
approach to exclude self-interaction. The sample specific capacitance
oscillations are in marked contrast to the charge relaxation resistance, which
together with the capacitance defines the RC-time, and which for spin polarized
electrons is quantized at half a resistance quantum. Both the capacitance
oscillations and the quantized charge relaxation resistance are seen in a
strikingly clear manner in a recent experiment.
