Stability measures in metastable states with Gaussian colored noise

We present a study of the escape time from a metastable state of an overdamped Brownian particle, in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise enhanced stability effect for all the initial unstable states used, and for all values of the correlation time $\tau_c$ investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noise respectively, depending on the value of $\tau_c$ with respect to the relaxation time of the system.Comment: 6 pages, 7 figure

Critical Phenomena and Diffusion in Complex Systems

Editorial of the International Conference on Critical Phenomena and Diffusion in Complex Systems held on 5--7 December, 2006 in Nizhniy Novgorod State University, Russia and was dedicated to the memory and 80th anniversary of Professor Askold N. Malakhov.Comment: 4 pages, to appear in International Journal of Bifurcation and Chao

Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources

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 behaviours 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 junction edges. Stochastic resonant activation, noise enhanced stability and temporary trapping phenomena are observed in the system investigated.Comment: 16 pages, 9 figures, Physical Review B, in pres

Uhlmann curvature in dissipative phase transitions

We study the mean Uhlmann curvature in fermionic systems undergoing a dissipative driven phase transition. We consider a paradigmatic class of lattice fermion systems in non-equilibrium steady-state of an open system with local reservoirs, which are characterised by a Gaussian fermionic steady state. In the thermodynamical limit, in systems with translational invariance we show that a singular behaviour of the Uhlmann curvature represents a sufficient criterion for criticalities, in the sense of diverging correlation length, and it is not otherwise sensitive to the closure of the Liouvillian dissipative gap. In finite size systems, we show that the scaling behaviour of the mean Uhlmann curvature maps faithfully the phase diagram, and a relation to the dissipative gap is put forward. We argue that the mean Uhlmann phase can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.Comment: 5 pages, 3 figures with appendix of 10 pages, 1 figur

Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime

We investigate the quantum dynamics of a multilevel bistable system coupled to a bosonic heat bath beyond the perturbative regime. We consider different spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic dissipation, and different cutoff frequencies. The study is carried out by using the real-time path integral approach of the Feynman-Vernon influence functional. We find that, in the crossover dynamical regime characterized by damped \emph{intrawell} oscillations and incoherent tunneling, the short time behavior and the time scales of the relaxation starting from a nonequilibrium initial condition depend nontrivially on the spectral properties of the heat bath.Comment: 16 pages, 7 figure

Quantum resonant activation

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multi-peaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency $\nu^*$ which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.Comment: 14 pages, 13 figure

Noise Enhanced Stability

The noise can stabilize a fluctuating or a periodically driven metastable state in such a way that the system remains in this state for a longer time than in the absence of white noise. This is the noise enhanced stability phenomenon, observed experimentally and numerically in different physical systems. After shortly reviewing all the physical systems where the phenomenon was observed, the theoretical approaches used to explain the effect are presented. Specifically the conditions to observe the effect: (a) in systems with periodical driving force, and (b) in random dichotomous driving force, are discussed. In case (b) we review the analytical results concerning the mean first passage time and the nonlinear relaxation time as a function of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise.Comment: 18 pages, 6 figures, in press Acta Physica Polonica (2004

Effects of L\'evy noise on the dynamics of sine-Gordon solitons in long Josephson junctions

We numerically investigate the generation of solitons in current-biased long Josephson junctions in relation to the superconducting lifetime and the voltage drop across the device. The dynamics of the junction is modelled with a sine-Gordon equation driven by an oscillating field and subject to an external non-Gaussian noise. A wide range of $\alpha$-stable L\'evy distributions is considered as noise source, with varying stability index $\alpha$ and asymmetry parameter $\beta$. In junctions longer than a critical length, the mean switching time (MST) from superconductive to the resistive state assumes a values independent of the device length. Here, we demonstrate that such a value is directly related to the mean density of solitons which move into or from the washboard potential minimum corresponding to the initial superconductive state. Moreover, we observe: (i) a connection between the total mean soliton density and the mean potential difference across the junction; (ii) an inverse behavior of the mean voltage in comparison with the MST, with varying the junction length; (iii) evidences of non-monotonic behaviors, such as stochastic resonant activation and noise enhanced stability, of MST versus the driving frequency and noise intensity for different values of $\alpha$ and $\beta$; (iv) finally, these non-monotonic behaviors are found to be related to the mean density of solitons formed along the junction.Comment: 24 pages, 8 figures, submitted to J. Stat. Mech.: Theory Exp. arXiv admin note: text overlap with arXiv:1406.481