We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency, and junction length. We observe that these nonmonotonic behaviors are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played by the formation and propagation of solitons, with two different dynamical regimes characterizing the dynamics of the phase string. Our analysis allows to evidence the effects of different bias current densities, that is a simple spatially homogeneous distribution and a more realistic inhomogeneous distribution with high current values at the edges. Stochastic resonant activation, noise-enhanced stability, and temporary trapping phenomena are observed in the system investigated.

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.

We investigate the superconducting lifetime of a long overdamped current-biased Josephson junction, in the presence of telegraph noise sources. The analysis is performed by randomly choosing the initial condition for the noise source. However, in order to investigate how the initial value of the dichotomous noise affects the phase dynamics, we extend our analysis using two different fixed initial values for the source of random fluctuations. In our study, the phase dynamics of the Josephson junction is analyzed as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive metastable state as a function of the noise intensity is characterized by nonmonotonic behavior, strongly related to the soliton dynamics during the switching towards the resistive state. The role of the correlation time of the noise source is also taken into account. Noise-enhanced stability is observed in the investigated system.

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system- bath coupling and the temperature, producing a stabilizing effect.