Phase-locked states in the system of two capacitively coupled Josephson junctions

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Abstract
The dynamics of two underdamped Josephson junctions coupled by a capacitance is studied analytically and numerically. Two types of stationary states are found for the system. Averaged voltages across the junctions have the same (nonzero) values for the first type of states, while for the second type the voltage across one of the junctions is equal to zero. The region of the synchronized dynamics is narrow and depends on the way of the current variation. The current-voltage characteristics shows negative differential resistance for the second type of states. The switching between different states by variation of applied currents is observed. Existence conditions for the phaselocking and parameters of synchronized oscillations are obtained analytically. The result of numerical calculations agrees with theoretical predictions.