Giovanni Filatrella

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, given 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 processes: a Gaussian contribution to simulate an uncorrelated ordinary thermal bath, and non-Gaussian, α-stable (or Lévy) term, generally associated to non-equilibrium transport phenomena. We find that the analysis of the switching current distribution makes it possible to efficiently detect a non-Gaussian noise component in a Gaussian background.

Generalized coupling in the Kuramoto model

We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays, and mechanical systems, where the active elements are turned on one by one. The resulting model is analytically tractable and predicts that both first and second order phase transitions are possible, depending upon the value of a new parameter that tunes the coupling among the oscillators. Numerical simulations of the model are in accordance with the analytical estimates, and in qualitative agreement with the behavior of Josephson junctions coupled via a cavity.

ON TECHNOLOGY COMPETITION: A FORMAL ANALYSIS OF THE ‘SAILING-SHIP EFFECT’

One of the key features of our economies consists of the coexistence of different technologies supplying similar products and services. We often observe that an old technology is improved when a new one appears; behind this process of improvement often lies an intentional research activity. There thus begins a competition between the two technologies whose performances are improved via R&D. We focus our attention on this competition process and supply a formal model, based on the optimization of R&D expenditure of both technologies, which can describe the dynamics of the delayed overtaking of the new technology over the old one.

On endogenous growth and increasing returns: modeling learning-by-doing and the division of labor

This paper discusses those sources of endogenous growth arising from labor as labor. It uses a production function which models the returns to scale as a function of the division of labor and learning. Smithian analysis of the labor process constitutes the basis upon which we build our own approach. The dynamics, therefore, drawn upon are more classical in style than those suggested by Arrow`s (1962) article.

Stochastic Bifurcations induced by correlated Noise in a Birhythmic van der Pol System

Abstract We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker–Planck equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.

Interplay between detection strategies and stochastic resonance properties

Abstract We discuss how to exploit stochastic resonance with the methods of statistical theory of decisions. To do so, we evaluate two detection strategies: escape time analysis and strobing. For a standard quartic bistable system with a periodic drive and disturbed by noise, we show that the detection strategies and the physics of the double well are connected, inasmuch as one (the strobing strategy) is based on synchronization, while the other (escape time analysis) is determined by the possibility to accumulate energy in the oscillations. The analysis of the escape times best performs at the frequency of the geometric resonance, while strobing shows a peak of the performances at a special noise level predicted by the stochastic resonance theory. We surmise that the detection properties of the quartic potential are generic for overdamped and underdamped systems, in that the physical nature of resonance decides the competition (in terms of performances) between different detection strategies.

Escape time characterization of pendular Fabry-Perot

In a pendular Fabry-Perot interferometer the system placed inside one of the minimum of the optomechanical potential undergoes an escape if it crosses the point of sudden change of reflectivity near the top of the potential well. We demonstrate that the loss of information that occurs retaining only the sequence of escapes, rather than the full trajectory, is mild if suitable signal processing techniques are applied to reveal the noise intensity or the presence of a coherent signal.

Pseudopotential of birhythmic van der Pol-type systems with correlated noise

We propose to compute the effective activation energy, usually referred to a pseudopotential or quasipotential, of a birhythmic system—a van der Pol-like oscillator—in the presence of correlated noise. It is demonstrated, with analytical techniques and numerical simulations, that the correlated noise can be taken into account and one can retrieve the low noise rate of the escapes. We thus conclude that a pseudopotential, or an effective activation energy, is a realistic description for the stability of birhythmic attractors also in the presence of correlated noise.

On delayed technological shifts

When a new technology capable of superseding an existing one appears, we sometimes observe the so-called sailing-ship effect, which consists of the old technologys improvements in response to the emergence of the new one. This helps explain why the old technology does not disappear quickly. However, some more aspects contribute to slowing down the process of substitution of the new for the old technology, such as users’ reluctance to switch to the new one, the degree of diffusion of the old technology, and other forces. In this work, we provide a formal model which takes into account both the technical improvements of the old technology as well as the other forces, where the latter are synthesised in what we define as a memory effect.

Two-dimensional Josephson junction arrays coupled through a high-Q cavity

The problem of disordered two-dimensional arrays of underdamped Josephson junctions is addressed. Our simulations show that when coupled to a high-Q cavity, the array exhibits synchronized behavior, and the power emitted can be considerably increased once enough junctions are activated to pump the cavity. The highly resonant cavity induces synchronized behavior, which is qualitatively different than what is familiar from other studies on nonlinear oscillator arrays, for example the Kuramoto model. We also address the effects of disorder, as well as the role of detuning between the spontaneous emission frequency of the junctions and the cavity resonant frequency. We show with a simple argument that we can predict the scaling behavior of disorder with the size of the array. The consequences for the design of microwave oscillators in the Gigahertz region are discussed.