Tunneling into one-dimensional Josephson chains and Luttinger liquids

One-dimensional arrays of Josephson junctions have been studied because of their unusual zero-temperature superconductor-insulator phase transitions. Furthermore, their low-energy Hamiltonian coincides with that of a Luttinger liquid. Hence 1-D Josephson junction arrays provide a physical realization of this model system. In order to explore these similarities we discuss 1-D arrays with defects, making contact to recent studies of transport in Luttinger liquids. We then study Andreev tunnelling between a Josephson chain and a normal metal and between a superconductor and a Luttinger liquid. In both cases, the current-voltage characteristics strongly deviate From a linear dependence.