TUNNELING IN THE ELECTRON BOX IN THE NONPERTURBATIVE REGIME

We study charging effects and tunneling in the single electron box. Tu nneling mixes different charge states and in the nonperturbative regim e the charge in the island may be strongly screened. When charge state s are nearly degenerate the screening of the charge is strong even in the weak tunneling regime. Virtual tunneling processes reduce both the level splitting Delta and the tunneling strength alpha. The charge on the island and the decay rates are calculated. In the strong tunnelin g regime also nondegenerate states are affected by tunneling. Strong-c oupling scaling renormalizes the effective capacitance, a result which we confirm by Monte Carlo simulations. The tunneling strength alpha s cales to smaller values into the regime where the weak-coupling scalin g applies. We propose a two-stage scaling procedure providing the unif ied picture for the problem. The scaling analysis is also extended to superconducting tunnel junctions with finite subgap conductance.