I-V Characteristics of an array of discrete Josephson junction and effect of a localized defect

In this paper, we present analytical and numerical studies of one-dimensional (1D) arrays of Josephson junctions. We use a perturbative approach to derive the I-V characteristics of the array and predict the appearance of current singularities. Numerical treatment gives a very close agreement with our analytical previsions when the discreteness parameter is small. A numerical study of junction with localized inhomogeneity in the Josephson critical current density is carried out. As a general trend, it comes out that these inhomogeneities conserve the linear branches as well as the current steps of the I-V characteristics. However, depending on the location of the defect and its type (microshort or microresistance), the range of the current steps varies and shows a peak at the middle of the array.