Claudio Guarcello - Università di Palermo # Noisy dynamics in long and short Josephson junctions # The transient dynamics of a noisy Josephson junction (JJ) is computationally explored, analyzing three different cases. First, the superconducting lifetime of a long JJ (LJJ) is investigated, analyzing its behavior as a function of the system and noise parameters. Specifically we study the dynamics of the parameter \(\phi\), i.e. the phase difference between the macroscopic wave functions in the two electrodes of the junction, whose dynamics is ruled by the perturbed sine-Gordon (SG) equation. We focus on the mean switching time (MST), calculated as a nonlinear relaxation time, from the superconducting metastable state to the resistive state. The dynamics of the phase difference \(\phi\) is studied in the presence of an external noise with different statistics, i.e. Gaussian, Cauchy-Lorentz and Lévy-Smirnov, implemented usin \(\alpha\)-stable (or Lévy) distributions. For proper values of the system parameters and different statistics of the noise source, the MST is characterized by non-monotonic trends. The study of the time evolution of \(\phi\) highlights the influence of noise induced solitons on the MST behavior. Moreover, in the presence of Lévy flights, another localized SG solutions, the breathers, can be detected. We also present a study on the exclusive breather generation in LJJ stimulated by an external driving signal. A breather is a bound pair of a soliton and an antisoliton oscillating with an internal frequency \(\omega\). Considerable amount of theoretical and computational studies, about breathers in LJJ, exists, despite of the absence of experimental works devoted to their detection. This study is devoted to establish an efficient experimental setting to generate a SG breather in a LJJ, exploiting a well-known phenomenon, the nonlinear supratransmission (NLS). In our model, one end of the junction is driven by a sinusoidal pulse of amplitude A and frequency \(\omega\) lower than the plasma frequency of the junction. In the 2D parameters space \((A, \omega)\), we observe a region where no NLS phenomena appear, that is no energy flow through the system is present. In other cases, in correspondence of specific \((A, \omega)\) values, we observe only breathers. Otherwise, different combinations of SG solutions propagate along the junction. The analysis is performed for different values of damping parameter, duration of the external driving and applied bias current. To check the robustness of the breathers generated, a Gaussian noise source is inserted into the perturbed SG model, and the percentage of surviving breathers is calculated. Finally, the phase dynamics in a short JJ, i.e. ballistic graphene-based JJ, is investigated. The phase dynamics is ruled by the Resistively and Capacitively Shunted Junction (RCSJ) model, here improved inserting a thermal noise contribute. The superconductor-graphene-superconductor system is characterized, as much as normal current biased JJs, by the presence of quantum metastable states. In this case, the mean first passage time (MFPT) from these metastable states is calculated in the presence of different sources of white or correlated Gaussian noise. MFPT data are obtained for different values of both noise intensity and frequency of the alternate current bias, observing noise induced phenomena.

In collaboration with: D. Valenti, B. Spagnolo, K. Fedorov, A. Ustinov

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