Kinetic inductance of Josephson-junction arrays: Dynamic and equilibrium calculations.

We show analytically that the inverse kinetic inductance L of an overdamped junction array at low frequencies is proportional to the admittance of an inhomogeneous equivalent impedance network. The ij bond in this equivalent network has an inverse inductance Jij cos(θ 0 i − θ 0 j − Aij), where Jij is the Josephson coupling energy of the ij th bond, θ i is the ground-state phase of the grain i, and Aij is the usual magnetic phase factor. We use this theorem to calculate L for square arrays as large as 180 × 180. The calculated L is in very good agreement with the low-temperature limit of the helicity modulus γ calculated by conventional equilibrium Monte Carlo techniques. However, the finite temperature structure of γ, as a function of magnetic field, is sharper than the zero-temperature L, which shows surprisingly weak structure. In triangular arrays, the equilibrium calculation of γ yields a series of peaks at frustrations f = 1 2 (1−1/N), where N is an integer ≥ 2, consistent with experiment. PACS numbers: 74.50.+r, 74.60.Ge, 74.60.Jg, 74.70.Mq Typeset using REVTEX