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 ₀V+ sigma ₁Vcos phi +j₁ sin phi , whose parameters sigma ₀, sigma ₁,j₁ 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.