Strong Tunneling in the Single-Electron Box

We study strong tunneling (i.e. transmission $h\mathrm{/}{e}^2{R}_T\gg 1$) in the single-electron box with many transverse modes at zero temperature. We develop a new renormalization group method which includes all charge states and requires no initial or final energy cutoff. We determine the ground-state energy, the average charge and the renormalized charging energy. The covered range for the coupling constant and the gate voltage is much increased in comparison to recent perturbative approaches, poor man scaling methods and Quantum Monte Carlo simulations. We reach the regime where Coulomb blockade become practically unobservable.