Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

Theory of dressed states in quantum optics

The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.Comment: Revtex, 17 page

Cooperative effects in Josephson junctions in a cavity in the strong coupling regime

We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally reached for a single junction. Rabi oscillations are obtained with the frequency proportional to integer order Bessel functions in the limit of a large photon number, similarly to the case of the single qubit. A selection rule is derived for the appearance of Rabi oscillations. A quantum amplifier built with a large number of Josephson junctions in a cavity in the strong coupling regime is also described.Comment: 9 pages, no figures. Version accepted for publication in Physical Review

The Chamaeleon II low-mass star-forming region: radial velocities, elemental abundances, and accretion properties

Radial velocities, elemental abundances, and accretion properties of members of star-forming regions (SFRs) are important for understanding star and planet formation. While infrared observations reveal the evolutionary status of the disk, optical spectroscopy is fundamental to acquire information on the properties of the central star and on the accretion characteristics. 2MASS archive data and the Spitzer c2d survey of the Chamaeleon II dark cloud have provided disk properties of a large number of young stars. We complement these data with spectroscopy with the aim of providing physical stellar parameters and accretion properties. We use FLAMES/UVES+GIRAFFE observations of 40 members of Cha II to measure radial velocities through cross-correlation technique, Li abundances by means of curves of growth, and for a suitable star elemental abundances of Fe, Al, Si, Ca, Ti, and Ni using the code MOOG. From the equivalent widths of the Halpha, Hbeta, and the HeI-5876, 6678, 7065 Angstrom emission lines, we estimate the mass accretion rates, dMacc/dt, for all the objects. We derive a radial velocity distribution for the Cha II stars (=11.4+-2.0 km/s). We find dMacc/dt prop. to Mstar^1.3 and to Age^(-0.82) in the 0.1-1.0 Msun mass regime, and a mean dMacc/dt for Cha II of ~7*10^(-10) Msun/yr. We also establish a relationship between the HeI-7065 Angstrom line emission and the accretion luminosity. The radial velocity distributions of stars and gas in Cha II are consistent. The spread in dMacc/dt at a given stellar mass is about one order of magnitude and can not be ascribed entirely to short timescale variability. Analyzing the relation between dMacc/dt and the colors in Spitzer and 2MASS bands, we find indications that the inner disk changes from optically thick to optically thin at dMacc/dt~10^(-10) Msun/yr. Finally, the disk fraction is consistent with the age of Cha II.Comment: 21 Pages, 15 Figures, 7 Tables. Accepted for publication in Astronomy and Astrophysics. Abstract shortene

Photospheric and chromospheric activity in four young solar-type stars

We present a photometric and spectroscopic study of four G-K dwarfs, namely HD 166, epsilon Eri, chi1 Ori and kappa1 Cet. In three cases, we find a clear spatial association between photospheric and chromospheric active regions. For chi1 Ori we do not find appreciable variations of photospheric temperature, and chromospheric Halpha emission. We applied a spot/plage model to the observed rotational modulation of temperature and flux to derive spot/plage parameters and to reconstruct a rough three-dimensional map of the outer atmosphere of kappa1 Cet, HD 166 and epsilon Eri.Comment: 12 pages, 3 tables, 9 figures. Submitted to Ap

Investigation of DC-8 nacelle modifications to reduce fan-compressor noise in airport communities. Part 2 - Design studies and duct-lining investigations, May 1967 - October 1969

Modifications to reduce fan-compressor noise level of DC-8 aircraft - Part

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Multitask Hopfield Networks

Multitask algorithms typically use task similarity information as a bias to speed up and improve the performance of learning processes. Tasks are learned jointly, sharing information across them, in order to construct models more accurate than those learned separately over single tasks. In this contribution, we present the first multitask model, to our knowledge, based on Hopfield Networks (HNs), named HoMTask. We show that by appropriately building a unique HN embedding all tasks, a more robust and effective classification model can be learned. HoMTask is a transductive semi-supervised parametric HN, that minimizes an energy function extended to all nodes and to all tasks under study. We provide theoretical evidence that the optimal parameters automatically estimated by HoMTask make coherent the model itself with the prior knowledge (connection weights and node labels). The convergence properties of HNs are preserved, and the fixed point reached by the network dynamics gives rise to the prediction of unlabeled nodes. The proposed model improves the classification abilities of singletask HNs on a preliminary benchmark comparison, and achieves competitive performance with state-of-the-art semi-supervised graph-based algorithms.Comment: 16 pages, 1 figure

PG 1613+426: a new sdB pulsator

We report the detection of short period oscillations in the hot subdwarf B (sdB) star PG 1613+426 from time-series photometry carried out with the 91-cm Cassegrain telescope of the Catania Astrophysical Observatory. This star, which is brighter than the average of the presently known sdB pulsators, with B = 14.14 mag, has $T_{\rm eff}=34 400 {\rm K}$ and $\log g = 5.97$, its position is near the hot end of the sdB instability strip, and it is a pulsator with a well observed peak in the power spectrum at $144.18\pm 0.06 \rm s$. This star seems to be well suited for high precision measurements, which could detect a possible multi-mode pulsation behaviourComment: 3 pages, 4 figures. to appear on A&