Noise-induced phenomena in transient dynamics of short and long Josephson junctions

The investigation of nonlinear properties of Josephson junctions (JJs) is very important due to their broad applications in logic devices. Currently, all Josephson junctions are manufactured with the use of optical and electronic lithography, and they can always be considered as distributed. Moreover great interest recently has attracted, from theoretical and experimentally point of view, the investigation of the influence of thermal fluctuations in macroscopic quantum phenomena of short and long Josephson junctions. Particularly the role of the noise on the life time of the superconductive state has been subject of many investigations. In fact for some devices, as the rapid single flux quantum devices (RSFQ), based on Josephson junctions, minimization of the switching time is required for better performance. In the frame of the resistive McCumber-Stewart model we analyze the transient dynamics of short and long overdamped Josephson junctions, in the presence both of a periodic driving force and a Gaussian autocorrelated noise. We use the archetypal source for colored noise, i. e. an exponentially correlated Ornstein-Uhlenbeck process. We focus our study on the behavior of the mean switching time (MST), and its standard deviation, from superconductive to resistive regime as a function of the colored noise parameters, i.e. noise intensity $\sigma$ and correlation time $\tau_c$. The resonant activation (RA) and the noise enhanced stability (NES) phenomena have been investigated with different noise parameters and bias current. In a short Josephson junction we find that fluctuations may both decrease and increase the mean switching time and that the positions both of the minimum of RA and the maximum of NES depend on the value of the noise correlation time $\tau_c$. Moreover in the frequency range where RA is observed, the mean switching time exhibits a non-monotonic behavior as a function of $\tau_c$. In order to take into account the spatial effects, we consider the phase values depending also on the space and, therefore, the stochastic dynamics of a long Josephson junction is investigated, in the frame of the sine-Gordon model. The influence of the length of the JJ on the mean switching time and on the above-mentioned noise induced phenomena (RA and NES), in the presence of colored noise, is analyzed. The influence of different bias currents on the MST is also investigated. Our results are discussed and compared with those obtained in the presence of white noise