Fractal properties of critical current of a self-similar system of Josephson junctions connected in parallel

Abstract

A fractal value (the local cell dimension Dc ) has been found to characterize the dependence of the maximum Josephson current square I² on the magnetic field in self-similar systems of Josephson junctions connected in parallel and separated by distances distributed like Cantor set of segments. The cell dimension has been shown to be related to the fractal system dimension D by the relationship Dc ≈ 2 - D, which had been checked for systems with the different fractal dimensions.