Nonequilibrium and relaxation effects in tunnel superconducting   junctions
  The specific property of a planar tunnel junction with thin-film diffusive plates and long enough leads is an essential enhancement of its transmission coefficient compared to the bare transparency of the tunnel barrier [1,2]. In voltage-biased junctions, this creates favourable conditions for strong nonequilibrium of quasiparticles in the junction plates and leads, produced by multiparticle tunneling. We study theoretically the interplay between the nonequilibrium and relaxation processes in such junctions and found that nonequilibrium in the leads noticeably modifies the current-voltage characteristic at $eV > 2\Delta$, especially the excess current, whereas strong diffusive relaxation restores the result of the classical tunnel model. At $eV \leq 2\Delta$, the diffusive relaxation decreases the peaks of the multiparticle currents. The inelastic relaxation in the junction plates essentially suppresses the $n$-particle currents ($n>2$) by the factor $n$ for odd and $n/2$ for even $n$. The results may be important for the problem of decoherence in Josephson-junction based superconducting qubits. 
E.V. Bezuglyi, A.S. Vasenko and E.N. Bratus'
cond-mat.supr-con