Abstract
We show that the Coulomb blockade in parallel dots pierced by magnetic flux Φ completely blocks the resonant current for any value of Φ except for integer multiples of the flux quantum Φ0. This non-analytic (switching) dependence of the current on Φ arises only when the dot states that carry the current are of the same energy. The time needed to reach the steady state, however, diverges when Φ→nΦ0.