Effects of Lévy 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 direc…

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…

Anomalous transport effects on switching currents of graphene-based Josephson junctions

We explore the effect of noise on the ballistic graphene-based small Josephson junctions in the framework of the resistively and capacitively shunted model. We use the non-sinusoidal current-phase relation specific for graphene layers partially covered by superconducting electrodes. The noise induced escapes from the metastable states, when the external bias current is ramped, give the switching current distribution, i.e. the probability distribution of the passages to finite voltage from the superconducting state as a function of the bias current, that is the information more promptly available in the experiments. We consider a noise source that is a mixture of two different types of proce…

Statistics of residence time for Lévy flights in unstable parabolic potentials

We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.

Nonlinear relaxation phenomena in metastable condensed matter systems

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 s…

THE ROLE OF NON-GAUSSIAN SOURCES IN THE TRANSIENT DYNAMICS OF LONG JOSEPHSON JUNCTIONS

We analyze the effects of different non-Gaussian noise sources on the transient dynamics of an overdamped long Josephson junction. We find nonmonotonic behavior of the mean escape time as a function of the noise intensity and frequency of the external driving signal for all the noise sources investigated.

Generation of travelling sine-Gordon breathers in noisy long Josephson junctions

The generation of travelling sine-Gordon breathers is achieved through the nonlinear supratransmission effect in a magnetically driven long Josephson junction, in the presence of losses, a current bias, and a thermal noise source. We demonstrate how to exclusively induce breather modes by means of controlled magnetic pulses. A nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. An experimental protocol providing evidence of the Josephson breather's existence is proposed.

ADSORPTION OF WATER MOLECULES ONTO 1:1 DIOCTAHEDRAL CLAY MINERALS: A BADER'S TOPOLOGICAL ANALYSIS OF THE AB-INITIO ELECTRON DENSITIES

Supratransmission-induced traveling breathers in long Josephson junctions

The emergence of travelling sine-Gordon breathers due to the nonlinear supratransmission effect is theoretically studied in a long Josephson junction driven by suitable magnetic pulses, taking into account the presence of dissipation, a current bias, and a thermal noise source. The simulations clearly indicate that, depending on the pulse's shape and the values of the main system parameters, such a configuration can effectively yield breather excitations only. Furthermore, a nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. Finally, the dynamics of the supratransmission-induced breathers is characterized by looking at quantit…

Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations

In this work we study by numerical methods the phase dynamics in ballistic graphene-based short Josephson junctions. The supercurrent through a graphene junction shows a non-sinusoidal phase-dependence, unlike a conventional junction ruled by the well-known d.c. Josephson relation. A superconductor-graphene-superconductor system exhibits superconductive quantum metastable states similar to those present in normal current-biased JJs. We explore the effects of thermal and correlated fluctuations on the escape time from these metastable states, when the system is stimulated by an oscillating bias current. As a first step, the analysis is carried out in the presence of an external Gaussian whit…

ELECTRONIC, MAGNETIC AND STRUCTURAL PROPERTIES OF NIO AND FEO THIN FILMS EPITAXIALLY GROWN ON SURFACES OF CU(001) : AN AB-INITIO DENSITY FUNCTIONAL STUDY

Ac-locking of thermally-induced sine-Gordon breathers

A complete framework for exciting and detecting thermally-induced, stabilized sine-Gordon breathers in ac-driven long Josephson junctions is developed. The formation of long-time stable breathers locked to the ac source occurs for a sufficiently high temperature. The latter emerges as a powerful control parameter, allowing for the remarkably stable localized modes to appear. Nonmonotonic behaviors of both the breather generation probability and the energy spatial correlations versus the thermal noise strength are found. The junction's resistive switching characteristics provides a clear experimental signature of the breather.

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

We propose a threshold detector for Lévy-distributed fluctuations based on a Josephson junction. The Lévy-noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of the zero-voltage state of the junction. We observe that the analysis of the cumulative distribution function of the switching currents supplies information on both the characteristics' shape parameter α of the Lévy statistics. Moreover, we discuss a theoretical model, which allows characteristic features of the Lévy fluctuations to be extracted from a measured distribution of switching currents. In view of these results, this system can effectively find an appl…

Noise-induced effects in nonlinear relaxation of condensed matter systems

Abstract Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuat…

Josephson-junction-based axion detection through resonant activation

We discuss the resonant activation phenomenon on a Josephson junction due to the coupling of the Josephson system with axions. We show how such an effect can be exploited for axion detection. A nonmonotonic behavior, with a minimum, of the mean switching time from the superconducting to the resistive state versus the ratio of the axion energy and the Josephson plasma energy is found. We demonstrate how variations in switching times make it possible to detect the presence of the axion field. An experimental protocol for observing axions through their coupling with a Josephson system is proposed.

Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influenc…

Voltage drop across Josephson junctions for L\'evy noise detection

We propose to characterize L\'evy-distributed stochastic fluctuations through the measurement of the average voltage drop across a current-biased Josephson junction. We show that the noise induced switching process in the Josephson washboard potential can be exploited to reveal and characterize L\'evy fluctuations, also if embedded in a thermal noisy background. The measurement of the average voltage drop as a function of the noise intensity allows to infer the value of the stability index that characterizes L\'evy-distributed fluctuations. An analytical estimate of the average velocity in the case of a L\'evy-driven escape process from a metastable state well agrees with the numerical calc…

Stabilization Effects of Dichotomous Noise on the Lifetime of theSuperconducting State in a Long Josephson Junction

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…

Analysis of soliton dynamics and noise induced effects on the superconductive lifetime in long Josephson junctions.

The influence of various noise sources on the transient dynamics of long Josephson junctions (LJJ) is investigated in the presence of an oscillating bias current signal and a noise source with Gaussian or non-Gaussian (i.e. Cauchy-Lorentz or Lévy-Smirnov) probability distributions. These systems are computationally analyzed integrating the perturbed Sine-Gordon equation describing the phase evolution. We found evidence of noise induced effects on trends of the mean escape time (MET) from the superconductive metastable state, varying different system parameters, as the bias frequency, noise intensity and junction length. In particular, we find resonant activation (RA) and noise enhanced stab…

Metastability and Relaxation in Quantum and Mesoscopic Systems

The transient dynamics and the relaxation of three quantum and mesoscopic systems are investigated. In particular we analyze: (i) a long Josephson junction (LJJ) driven by a non-Gaussian Lévy noise current; (ii) a metastable quantum dissipative 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. Specifically, in the first system the LJJ phase evolution is described by the perturbed sine-Gordon equation. We find the noise enhanced stability and resonant activation phenomena, by investigating the mean escape time as a function of the bias current frequency, noise intensity and length of…

Transient dynamics in driven long Josephson junctions.

The switching time from the superconductive metastable state of a long Josephson junction (LJJ)[1] is computationally analyzed in the framework of the perturbed sine-Gordon equation. The model includes an external bias current term and a stochastic noise source, i.e. a Lévy noise term. The effects of this noise on the mean escape time (MET) from the superconductive state are analyzed. The investigation is performed by considering a wide range of values of system parameters and different noise statistics: Gaussian, Cauchy-Lorentz and Lévy-Smirnov[2]. We found evidence of well known noise induced phenomena on the MET behavior, that is the noise enhanced stability (NES) and resonant activation…