Charge fluctuations in the single-electron box - art. no. 125307

Quantum fluctuations of the charge in the single-electron box are investiga ted. Based on a diagrammatic expansion we calculate the average island char ge number and the effective charging energy in third order in the tunneling conductance. Near the degeneracy point where the energy of two charge stat es coincides, the perturbative approach fails, and we explicitly resum the leading logarithmic divergencies to all orders. The predictions for zero te mperature are compared with Monte Carlo data and with recent renormalizatio n group results. While good agreement between the third-order result and nu merical data justifies the perturbative approach in most of the parameter r egime relevant experimentally, near the degeneracy point and at zero temper ature the resummation is shown to be insufficient to describe strong tunnel ing effects quantitatively. We also determine the charge noise spectrum by employing a projection operator technique. Former perturbative and semiclas sical results are extended by the approach.