I-V characteristics and stationary dynamics of a Josephson junction including the interference term in the current phase relation

The equation of motion for a local Josephson junction is solved assuming a current phase relation j z = sigma 0 V+ sigma 1 Vcos phi +j 1 sin phi , whose parameters sigma 0 , sigma 1 ,j 1 are calculated as appropriate averages from BCS weak-coupling theory. Analytical solutions can be given in the case of strong and weak damped junctions, the latter even for small currents. The I-V characteristics and the stationary dynamics are discussed for various damping parameters and relative conductivities. The critical current as a function of these quantities is also investigated.