KINETIC INDUCTANCE OF JOSEPHSON-JUNCTION ARRAYS - DYNAMIC AND EQUILIBRIUM CALCULATIONS

The low-frequency inverse kinetic inductance L(-1) of an overdamped ju nction array at temperature T = 0 is shown to equal that of an equival ent impedance network. The ijth bond of the network has an inverse ind uctance (2eE(ij)/($) over bar h) cos(theta(i)(0)-theta(j)(0)-A(ij)), w here E(ij) is the Josephson coupling energy of the ijth bond, se is th e ground-state phase of the grain i, and A(ij) is the usual magnetic p hase factor. Using this theorem, we calculate L(-1) for square lattice s as large as 180 x 180. The calculated L(-1) agrees well with the T = 0 limit of the helicity modulus gamma calculated by conventional Mont e Carlo techniques. In triangular arrays, the Monte Carlo calculation of gamma yields a series of peaks at frustrations f = 1/2(1-1/N), wher e N is an integer greater than or equal to 2, consistent with experime nts.