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 Keldysh technique we develop a regular perturbation theory in R}=1-{\mathcal and derive first order correction to current across link which consists two different contributions. One them is negative effectively corresponding decrease excess small $V$ due breaking multiple Andreev reflection cycle by normal for some quasiparticles. These quasiparticles, turn, generate second -- Josephson-like contribution increases decreasing down very where R}$ ceases be valid. Some above features are reproduced within physical picture involving Landau-Zener tunneling between states.