Impulsive current-induced superconducting junction in spatially broken symmetry of fluxons

Embarking upon McCumber–Stewart model, the temporal evolution of a superconducting Josephson junction in both overdamped and underdamped regimes is examined. The junction is driven by a pulse train current, and the potential of the tunnelling fluxons is assumed to lack spatial symmetry such that associated with a ratchet potential. In this respect, Langevin and Fokker–Plank-like equations specifying the junction are solved for which, time-dependent phase solutions are obtained and discussed on the basis of the potential broken symmetry and pulse signal properties by which, an ad hoc value of the frequency equals to the fractal Hausdorff dimension ω = DH = ln(2)/ln(3) = 0.630929753 of a normal Cantor set is ascribed.