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By means of numerical simulations we study the dynamics of the phase difference in faceted long Josephson junctions. We compare our simulations with experiments on a sample of high quality high-Tc biepitaxial junctions. Adjusting junction length and dissipation to reproduce the observed data we found a significant agreement, which permits to identify the observed resonances mostly as Eck steps. Some considerations are also made on the requirements to observe flux-flow or Fiske resonances in these junctions.

Chaotic dynamics in a model of a long Josephson junction (LJJ) is studied via standard techniques of non-linear maps. A characterization of chaos in such objects in terms of Lyapunov exponents and Poincare sections is given. Finally the occurrence of chaos in map dynamics is compared with preliminary results of full numerical integration of the perturbed sine-Gordon equation (PSGE).

The influence of surface-resistance dissipation on phase locking of fluxon oscillations in long Josephson junctions of in-line geometry subjected to microwave fields which interact with the fluxon at the junction boundaries is studied by the perturbation- theory map approach and by full integration of the pde model of the junction.

The status of advancement of the VIRGO Project is presented: the first-generation results from the Pisa seismic noise super attenuator give an upper limit to the noise transfer function of 2 × 10 −8 at 10 Hz. The upper limit to the absolute noise of the 400 kg test mass at 10 Hz has been measured to be 1.5 × 10 −13 m/√Hz. The scheme and the related problems of the VIRGO interferometer, which is supposed to work down to 10 Hz, are also presented. At the 3rd Pisa Meeting in 1986 we presented the idea of what could be a very efficient seismic noise reduction system able to give a sensitivity h ∼ 10 −25 at 10 Hz, in a 3 km interferometer for 1 year integration time. Now we have two new facts to present: the first is that the attenuation has been built, is working in Pisa, and shows remarkable characteristics. The second is the Italian-French interferometer VIRGO [1,2], a 3 km long antenna for low and high frequency (10–1000 Hz) gravitational wave (GW) detection. These two items will be presented in this article.

We study classical resonant activation (CRA) for a Josephson junction embedded in a shell circuit consisting of one capacitive and one inductive element. The low dissipation quality factor of this device is calculated analytically at the fundamental frequency for two different models of the shell circuit. From our numerical results it emerges that CRA and energy level quantization (ELQ) are distinct processes that can be distinguished in measurements on Josephson devices at low temperatures. CRA at subharmonic frequencies is a highly nonlinear process very different from the corresponding quantum multiphoton process. These results are relevant for the interpretation of a recent experiment on ELQ in high-temperature superconductors Josephson junctions.

We study the vortex-vortex and vortex-antivortex interaction in arrays of Josephson junction particularly addressing the effect of mutual induction in the intermediate screening ranges (betaa = 0.5). The modifications of the barrier energy for the displacement of a vortex in presence of a second vortex (antivortex), or more vortices (antivortices), are derived in an "adiabatic" approach. To this end, we have developed a fast explicit algorithm, which permits to retrieve the phases and the magnetization of the array in a reasonable time and with little memory occupation for relatively large arrays [e.g. o(100 times 100)]. This new model is able to catch the essential characters of the more complex "fully mutual coupling" model. We provide also some indications on the relation between energy barriers and the observation of vortex quantum tunneling phenomena in Josephson arrays and related systems as high-TC films.

We have observed energy level quantization in an all high critical temperature superconductor d-wave Josephson junction. From the measurements we have also extracted the quality factor Q of the junction which is of the order of 40. These results indicate that the role of dissipation mechanisms in high temperature superconductors has to be revised, and may also have consequences for the class of solid state ‘‘quiet’’ quantum bit with longer coherence time.

We have measured the energy level separation from the ground state to the first excited state in a high critical temperature superconductor d-wave Josephson junction. We observe that the bias current dependence of the energy level separation is strongly affected by the large shunt capacitance and inductance of the junction electrodes. In order to describe the effect of a shunt capacitance and shunt inductance on the junction dynamics we derive the equation of motion of the total system. In general such a circuit displays two resonance frequencies corresponding to two different energy scales. We discuss various limits for the values of the shunt inductor and capacitor.

Here we present the direct observation of macroscopic quantum properties in an all high-critical-temperature superconductor d-wave Josephson junction. Although dissipation caused by low-energy excitations is expected to strongly suppress macroscopic quantum effects, we demonstrate energy level quantization in our d-wave Josephson junction. The result indicates that the role of dissipation mechanisms in high-temperature superconductors has to be revised, and it may also have consequences for the class of solid-state “quiet” quantum bits with superior coherence time.

The effect of a perpendicular magnetic field on a disordered two‐dimensional Josephson junction array (JJA) is analyzed using numerical simulation of full mutual inductance array equations. Disordered JJA can represent either itself or a model for granular high‐Tc disordered thin films. In usual zero field cooling conditions and absence of disorder the field penetrate the sample following a Bean critical state model. Using a simple technique it is also possible to obtain the whole 3D field map around the array. It can be shown that disorder induces a scattering of flux lines giving rise to some flux penetration into the sample. The 3D field can be used to produce 2D images of the field intensity to be compared with existing magnetic imaging techniques. We briefly discuss the comparison of simulated images with existing imaging experiments, as SQUID Scanning Microscopy (SSM) and Magneto‐Optical techniques (MO).

A novel dynamical state has been observed in the dynamics of a perturbed sine-Gordon system. This resonant state has been experimentally observed as a singularity in the dc current-voltage characteristic of an annular Josephson tunnel junction, excited in the presence of a magnetic field. In this respect it can be assimilated to self-resonances known as Fiske steps. Differently from these, however, we demonstrate, on the basis of numerical simulations, that its detailed dynamics involves rotating fluxon pairs, a mechanism associated, so far, to self-resonances known as zero-field steps. This occurs because the size of nonlinear excitations is comparable with that of the system.

Recent experiments on high-temperature superconductors show paramagnetic behavior localized at grain boundaries (GB). This paramagnetism can be attributed to the presence unconventional d-wave induced $\pi$-junctions. By modeling the GB as an array of $\pi$ and conventional Josephson junction we determine the conditions of the occurrence of the paramagnetic behavior., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

In the last few years the return current, i.e., the value of the bias current where an hysteretic Josephson junction switches back to zero voltage state, has obtained interest in view of its connections with the evaluation of losses for macroscopic quantum coherence experiments and the following development of q-bit devices. Here we study carefully the problem of the return current by means of numerical simulations of associated Langevin equations in both very small and intermediate length Josephson junctions. Comparison with theoretical lifetime, fluctuations, and recent experiments are carefully carried out. The results show that the effects of finite length are important in the correct description of the return switch.

Recent considerations on the physics of YBa 2 Cu 3 O 7-δ films made possible explaining their transport properties as flow of supercurrents through links between the granular structure of the film. The present work deals with the analysis of the Josephson junction network as a discrete set of parallel junctions (1D array) in quasi-static conditions and is aimed to compare the results of the simulations with the experimental findings, in particular with the plateau-like features in the critical current dependence on the magnetic field. Different regimes and vortex phases have been individuated and discussed.

A connection between the disorder in the critical currents of two-dimensional arrays of Josephson junctions and the amount of phase-locking of a row to an external microwave signal is proposed. We have computed the probability of phase-locking as a function of the spread of the critical currents of the individual junctions. The analytic results are in good agreement with numerical simulations. The predictions can be also qualitatively compared to the experiments.

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed an explicit set of differential equations. We have found that the discretization parameter βL - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full model with mutual inductances, while the limits for very large and very small values of βL they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., small βL as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large βL).

We evaluate how the curvature dependence of surface tension affects the shape of electrically charged interfaces between a perfectly conducting fluid and its vapour. We consider two cases: i) spherical droplets in equilibrium with their vapour; ii) menisci pending in a capillary tube in presence of a conducting plate at given electric potential drop. Tolman-like dependence of surface tension on curvature becomes important when the "nucleation radius" is comparable with the interface curvature radius. In case i) we prove existence of the equilibrium minimal radius and estimate its dependence on the electric field and Tolmanlike curvature effects. In case ii) the menisci are subject to the gravitational force, surface tension and electrostatic fields We determine the unknown surface of the menisci to which the potential is assigned using an iterative numerical method and show that Tolman-like corrections imply: 1) a variation of the height (up to 10% in some cases) of the tip of the menisci; 2) a decrease of the maximum electrical potential applicable to the menisci before their breakdown amounting to 40V over 800V in the considered cases. We conjecture that these effects could be used in new experiments based on electric measurements to determine the dependence of the equilibrium surface tension on curvature, pages 17

Two-dimensional square arrays of short Josephson junctions are investigated using a model which includes both the lumped Josephson circuit elements and an equivalent inductance for the superconducting loops. We have supposed that all junction parameters and the inductances are identical. The analysis of the Gibbs thermodynamic potential shows the existence of energy barriers for a basic process for the diamagnetic behavior of the array: The motion of a flux quantum in the interior of the array. These barriers have been numerically evaluated as a function of the array parameters. The effect of the bias current is discussed and the critical current of the array has been estimated.

Suppression of temporal phase locked chaos in the perturbed sine-Gordon system is demonstrated by numerical simulations of the full equation in the presence of two harmonic signals. Results have been compared with a simple perturbative approach for the soliton dynamics.

We report on the fabrication procedure and the transport properties of submicron grain boundary biepitaxial YBCO Josephson junctions. These first results are very encouraging and justify further expectations on improved performances for such types of devices. A reduced and more controlled faceting along the grain boundary interface, for instance, will better preserve intrinsic d-wave effects, and favour the study of fluxons dynamics.

We analyse the diamagnetic behaviour of high Tc superconducting granular samples by mean of an equivalent network of Josephson junctions and inductances. The range of validity of the current approaches is determined by considering the complete expression for the Gibbs thermodynamic potential and by identifying two characteristic parameters β1 and β2 for these systems. A graphical representation of the validity limits of various current approaches and in particular of the superconducting glass model is given in a β1-β2 plane.