Josephson dynamics at high transmissions: Perturbation theory

We theoretically analyze Josephson dynamics of superconducting weak links with transmissions ${\mathcal T}$ not much smaller than unity at subgap bias voltages $V$. Employing the effective action approach combined with the Keldysh technique we develop a regular perturbation theory in ${\mathcal R}=1-{\mathcal T}$ and derive the first order correction to the current across the weak link which consists of two different contributions. One of them is negative effectively corresponding to a decrease of the excess current at small $V$ due to breaking of the multiple Andreev reflection cycle by normal reflection for some subgap quasiparticles. These quasiparticles, in turn, generate the second -- Josephson-like -- contribution to the current which increases with decreasing $V$ down to very small voltages where the perturbation theory in ${\mathcal R}$ ceases to be valid. Some of the above features are not reproduced within the physical picture involving Landau-Zener tunneling between subgap Andreev states.