Exact calculation of Shapiro step sizes for pulse-driven Josephson junctions

A nonperturbative solution is presented for the current-voltage characteristics of Josephson junctions driven by square-wave and periodic \ensuremath{\delta}-function signals. We find that no resonance conditions are required for the appearance of Shapiro steps--they appear for almost all amplitudes and frequencies of the driving pulse. Our calculations also permit a calculation of the boundaries of the Shapiro steps.