The problem of true macroscopic charge quantization in the Coulomb blockade

Based on the Ambegaokar-Eckern-Schön approach to the Coulomb blockade we develop a complete quantum theory of the single electron transistor. We identify a previously unrecognized physical observable in the problem that, unlike the usual average charge on the island, is robustly quantized for any finite value of the tunneling conductance as the temperature goes to the absolute zero. This novel quantity is fundamentally related to the non-symmetrized current noise of the system. Our results display all the super universal topological features of the θ-angle concept that previously arose in the theory of the quantum Hall effect.