Deterministic hopping in a Josephson circuit described by a one-dimensional mapping

Analog simulations of the hopping noise of a current-biased Josephson tunnel junction shunted with an inductor in series with a resistor reveal a 1/{ω} spectral density over two decades of frequency {ω} for a narrow range of bias currents. The amplitude of the low-frequency part of the spectrum decreases when white noise, representing Nyquist noise in the resistor at a few degrees Kelvin, is added to the simulation. We explain the shape of the power spectrum and its dependence on bias current and added white noise in terms of a deterministic process, involving a one-dimensional mapping, that is analogous to that found in Pomeau-Manneville intermittency. Moreover, we are able to establish a detailed relationship between the origin of the mapping and the differential equation describing the dynamics of the system.