Pairing collective modes in superfluid nuclei: a semiclassical approach

Collective pairing excitations in superfluid nuclei are studied by using the semiclassical time-dependent Hartree-Fock-Bogoliubov equations of motion in a linear approximation. It is found that the strength function associated with the semiclassical anomalous density response function has a resonance structure with a sharp peak around double energy gap that displays the monopole pairing collective mode.     

Deformation Techniques for Sparse Systems

We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system. This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration. Research was partially supported by the following grants: UBACyT X112 (2004–2007), UBACyT X847 (2006–2009), PIP CONICET 2461, PIP CONICET 5852/05, ANPCyT PICT 2005 17-33018, UNGS 30/3005, MTM2004-01167 (2004–2007), MTM2007-62799 and CIC 2007–2008.     

Analysis of Transmission Performance in SUPERPONs

In this work we study how optical amplifiers can deeply improve the performance of the passive optical networks (PONs), permitting a large number of optical network units (ONUs), transmitting at high bit rate. These high-capacity networks are called SUPERPONs, and we show how to achieve a network with 8,192 ONUs with a transmission in the downstream direction up to 10 Gbit/s.     

Experiments on 40 Gb/s Transmission with Wavelength Conversion: Results from the IST ATLAS Project

In this article we report the main experimental results obtained in the framework of the IST ATLAS project regarding the transmission at 40 Gb/s over long terrestrial links, including the frequency conversion of a signal. We report the single-channel 40 Gb/s transmission over a link 500 km long with an amplifier spacing of 100 km, both with G.652 fibers and G.653 fibers by periodically compensating the chromatic dispersion with dispersion-compensating fibers. We report the single-channel transmission at 40 Gb/s, also, after the wavelength conversion of a channel with both PPLN and semiconductor optical amplifier devices. In particular, 500 km distances are obtained with PPLN wavelength conversion and 300 km distances with semiconductor optical amplifiers. Some results have been reported for electronic devices operating at 40 Gb/s.     

10 Gbits−1 optically amplified single-channel systems operating in links encompassing conventional step-index fibres

In this work a numerical investigation is reported on the propagation regimes that allow single-channel systems to obtain the maximum capacity in links with optical amplification encompassing conventional step-index fibres. Solitons and NRZ signals are considered. We show how the periodical introduction of pieces of dispersion compensating fibres can greatly improve the system performance. The polarization properties of the signals are investigated to increase the system performance and     

Electric polarizability of small metal spheres

The electric polarizability of small sodium spheres is calculated in a semiclassical approximation based on the spherical jellium model and on the Vlasov equation. Static and dynamic polarizabilities are compared for two kinds of mean field with a smooth and a sharp surface. It is deduced that the position of the centroid of the surface-plasmon resonance is not sensitive to the surface diffuseness of the mean field. Comparison with analogous quantum calculations suggests that an unrealistic feature of the zero-range exchange-correlation force employed in the local-density approximation might play an important role in increasing the static polarizability and decreasing the frequency of the surface-plasmon resonance.     

Intrachannel nonlinearity enhancement in polarization multiplexed phase modulated systems with differential detection

We compare nonlinear impairments in phase-modulated transmission with and without polarization multiplexing. Using an analytic approach that enabled us to accurately predict the Q factor at the receiver, we show that, without polarization multiplexing, the differential receiver is insensitive to two-pulse cross phase modulation, whereas with polarization multiplexing two-pulse interaction between cross-polarized components causes significant performance degradation.     

The Hardness of Polynomial Equation Solving

Elimination theory was at the origin of algebraic geometry in the nineteenth century and now deals with the algorithmic solving of multivariate polynomial equation systems over the complex numbers or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e., polynomial equation systems) and admitting the representation of certain limit objects. Our main result is the following: let there be given such a data structure and together with this data structure a universal elimination algorithm, say P, solving arbitrary parametric polynomial equation systems. Suppose that the algorithm P avoids unnecessary branchings and that P admits the efficient computation of certain natural limit objects (as, e.g., the Zariski closure of a given constructible algebraic set or the parametric greatest common divisor of two given algebraic families of univariate polynomials). Then P$ cannot be a polynomial time algorithm. The paper contains different variants of this result and discusses their practical implications.