Abstract
We show that the single-particle polaron Green's function describes SIS tunnelling in cuprates, including the absence of Ohm's law at high voltages, the dip/hump features in the first derivative of the current, a substantial incoherent spectral weight beyond quasiparticle peaks and the unusual shape of the peaks. The theory allows us to determine the characteristic phonon frequency, coupling constant, normal and superconducting gap, and the impurity scattering rate.