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In this work we study by numerical methods the phase dynamics in ballisticgraphene-based short Josephson junctions. The supercurrent through a graphenejunction shows a non-sinusoidal phase-dependence, unlike a conventionaljunction ruled by the well-known d.c. Josephson relation. Asuperconductor-graphene-superconductor system exhibits superconductive quantummetastable states similar to those present in normal current-biased JJs. Weexplore the effects of thermal and correlated fluctuations on the escape timefrom these metastable states, when the system is stimulated by an oscillatingbias current. As a first step, the analysis is carried out in the presence ofan external Gaussian white noise source, which mimics the random fluctuationsof the bias current. Varying the noise intensity, it is possible to analyze thebehavior of the escape time from a superconductive metastable state indifferent temperature regimes. Noise induced phenomena, such as resonantactivation and noise induced stability, are observed. The study is extended tothe case of a coloured Gaussian noise source, analyzing how the escape timefrom the metastable state is affected by correlated random fluctuations fordifferent values of the noise correlation time.

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