Abstract
The existence of current-driven phase transitions in Josephson junction systems is treated using an analytic theory. An arbitrary impedance in parallel with the junction is included. The theory is a singular perturbation expansion around the known solutions for a resistively shunted junction. A number of multistable solutions can occur, depending on the external resonances and their Q values. The results are calculated specifically in the case of a single junction coupled to a waveguide. The nature of the transitions that occur during a current sweep is predicted to depend crucially on the relative sizes of the junction shunt resistance and the waveguide characteristic impedance. Good agreement with experimental observations of multistability is obtained when the series inductance of the shunt resistor is included. This decreases the effective Q of the waveguide at high input current levels, giving an extended multistable region relative to the case of no series inductance. The transitions that occur for nearly equal shunt resistance and characteristic impedance appear to offer the potential for high-speed frequency-modulated switching devices.
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