Some analytical results for the resistively shunted Josephson junction

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Abstract
Some analytical results for the resistively shunted Josephson junction, fed with an ac current in addition to a dc current, are reported. The original nonlinear differential equation for the phase difference of the order parameter is transformed to a linear second order differential equation with periodic coefficients. From this equation the possibility for harmonic current steps and the absence of subharmonic steps may be inferred. Furthermore, for low values of the ac current amplitude and frequency the step height of the first few steps is calculated in the tight binding approximation. At high frequencies the free electron approximation is used for the evaluation of the step heights for arbitrary values of the amplitude ; it follows that the step heights behave like Bessel functions. These results are qualitatively in agreement with numerical calculations by Russer and others

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