Advanced models of Josephson junction arrays (exchanged with TT 11.9)

One-dimensional Josephson junction arrays are interesting in many contexts. For instance, they can undergo quantum phase transitions, but they can also be used as a tunable environment in the study of other tunnel junctions or SQUIDs. Here we investigate a model for the array, which besides the Josephson junction and capacitance to ground additionally includes a stray inductance for each array element. For certain parameters, the dynamics of the system change drastically: In the phase regime, the impedance becomes purely imaginary in a parameter-dependent frequency range. We further find a gap in the dispersion relation for the same frequency range. We suggest a modified array with two different junctions per array element, in which this behaviour can be observed more easily