A mechanism for randomness

We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present real physical systems that can produce this kind of random time-series. We report the results of real experiments with nonlinear circuits containing direct evidence for this new phenomenon. In particular, we show that a Josephson junction coupled to a chaotic circuit can generate unpredictable dynamics. Some applications are discussed.