Oscillatory instabilities in d.c. biased quantum dots

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We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantum dot; these would constitute an experimental signature of the predicted effect.