Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations

We study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased Josephson junctions. We investigate the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is driven by an oscillating bias current in the presence of Gaussian white and colored noise sources. Varying the intensity and the correlation time of the noise source, it is possible to analyze the behavior of the escape time, or switching time, from a superconductive metastable state in different temperature regimes. Moreover, we are able to clearly distinguish dynamical regimes characterized by the dynamic resonant activation effect, in the absence of noise source, and the stochastic resonant activation phenomenon induced by the noise. For low initial values of the bias current, the dynamic resonant activation shows double-minimum structures, strongly dependent on the value of the damping parameter. Noise-enhanced stability is also observed in the system investigated. We analyze the probability density function (PDF) of the switching times. The PDFs for frequencies within the dynamic resonant activation minima are characterized by single peaks with exponential tails. The PDFs for noise intensities around the maxima of the switching time, peculiarity of the noise-enhanced stability phenomenon, are composed of regular sequences of two peaks for each period of the driving current, with exponentially decaying envelopes.