Charge-vibration interaction effects in normal-superconductor quantum dots

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal-conducting and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency ?. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime ?