An asymptotic solution for the resistively shunted junction (RSJ) model of the Josephson junction

Using the method developed by Bogolyubov et al., we find analytically a steady-state solution for the resistively shunted junction (RSJ) model of the Josephson junction that is driven by a constant current source. This solution explains how the relative amplitude of the voltage oscillation depends on the junction parameters such as I ₀ (the critical current), R (the resistance), C (the capacitance), and the external current I _e . The validity of the analytical solution is assessed by comparing it with numerical results. We find that this solution is useful for normal tunnel junction with I _e /I ₀ of order 1 or larger, and for any other weak links with I _e /I ₀ much larger than 1.