Noise phenomena and soliton dynamics in long Josephson junctions

In this work we computationally explore the transient dynamics of a noisy Josephson junction (JJ). Principal purpose is to investigate the behavior of the lifetime of the superconductive state as a function of the system and noise source parameters. The relations between the emerging phenomena and the evolution of the JJ order parameter \u3c6, that is the phase difference between the macroscopic wave functions describing the superconducting condensate in the two electrodes, is deeply investigated. We focus our interest on the switching events from the superconducting metastable state, and in particular on the mean escape time (MET). In the used model, a long JJ can be represented by a string composed by a series of phase cells rolling down on a tilted potential, commonly called the washboard potential. Different statistics are used to modelize the noise source, ranging from a Gaussian, to simulate a thermal bath, to a non-Gaussian (Cauchy-Lorentz or L\ue9vy-Smirnov) to include random fluctuations of external current signals. Their representation is made using an \u3b1-stable (or L\ue9vy) distribution, allowing to describe real situations in which typical trajectories of the noise source show abrupt jumps with very rapid variations of parameters, called L\ue9vy flights. Analysis of MET behavior reveals, for proper values of system parameters and statistic of noise source, the presence of clear non-monotonic trends. In particular, MET vs \u3b3 (noise intensity) data can show one or two maxima, effect known as noise enhanced stability (NES), and MET vs \u3c9 (frequency of the oscillating bias current) data present a pronounced minimum, effect known as resonant activation (RA). Other interesting results are obtained analyzing the MET behavior as a function of the junction length L. Also in this case we discover new behaviors. In particular, we note the presence of a characteristic length, after which the MET reaches asymptotically a constant value. For junctions with length greater then this particular value, the solitons can appear, but the overall transition dynamics is independent of the JJ length. All the analyses are performed using: (i) a constant homogenous bias current distribution, and (ii) an inhomogeneous distribution with current values rapidly increasing near the edges of the string. This allow us to take into account the more realistic situation in which the current flows through the junction, preferentially along its edges. These parts of the string act as soliton generators. The analysis of the time evolution of \u3c6 highlights the influence of the noise induced solitons on the MET behavior, and the presence of breathers generated by L\ue9vy flights. These mechanisms are responsible for switching events