Nonlinear relaxation in quantum and mesoscopic systems

The nonlinear relaxation of three mesoscopic and quantum systems are investigated. Specifically we study the nonlinear relaxation in: (i) a long Josephson junction (LJJ) driven by a non-Gaussian Lévy noise current; (ii) a metastable quantum open system driven by an external periodical driving; and (iii) the electron spin relaxation process in n-type GaAs crystals driven by a fluctuating electric field. In the first system the LJJ phase evolution is described by the perturbed sine-Gordon equation. Two well known noise induced effects are found: the noise enhanced stability and resonant activation phenomena. We investigate the mean escape time as a function of the bias current frequency, noise intensity and length of the junction. Moreover, the role of the soliton dynamics, induced by the noise on the switching events of the LJJ, is highlighted. In the second system, the asymptotic population of the metastable state as a function of the bath temperature, coupling strength and parameters of the external driving, that is frequency and amplitude, is analyzed in the framework of Caldeira-Leggett model and discrete variable representation. The asymptotic population of the metastable state, as a function of the driving frequency, displays a strong non monotonic behavior with a maximum, showing a quantum noise induced stability effect. Finally, the electron spin relaxation process is analyzed in the presence of two different sources of fluctuations: (a) a symmetric dichotomous noise and (b) a Gaussian correlated noise. Monte Carlo numerical simulations show, in both cases, an enhancement of the spin relaxation time by increasing the amplitude of the external noise. Moreover, we find that the electron spin lifetime versus the noise correlation time shows: (a) a monotonic increasing behavior in the case of dichotomous random fluctuations, and (b) a nonmonotonic behavior with a maximum in the case of bulks subjected to a Gaussian correlated noise.