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Quantum fluctuations of the charge in the single electron box areinvestigated. Based on a diagrammatic expansion we calculate the average islandcharge number and the effective charging energy in third order in the tunnelingconductance. Near the degeneracy point where the energy of two charge statescoincides, the perturbative approach fails, and we explicitly resum the leadinglogarithmic divergencies to all orders. The predictions for zero temperatureare compared with Monte Carlo data and with recent renormalization groupresults. While good agreement between the third order result and numerical datajustifies the perturbative approach in most of the parameter regime relevantexperimentally, near the degeneracy point and at zero temperature theresummation is shown to be insufficient to describe strong tunneling effectsquantitatively. We also determine the charge noise spectrum employing aprojection operator technique. Former perturbative and semiclassical resultsare extended by the approach.Comment: 20 pages, 15 figure

Charge fluctuations in the single-electron box