The effective neutrino charge radius

It is shown that at one-loop order a neutrino charge radius (NCR) may be defined, which is ultraviolet finite, does not depend on the gauge-fixing parameter, nor on properties of the target other than its electric charge. This is accomplished through the systematic decomposition of physical amplitudes into effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. In this way the NCR stems solely from an effective proper photon-neutrino one-loop vertex, which satisfies a naive, QED-like Ward identity. The NCR so defined may be extracted from experiment, at least in principle, by expressing a set of experimental electron-neutrino cross-sections in terms of the finite NCR and two additional gauge- and renormalization-group-invariant quantities, corresponding to the electroweak effective charge and mixing angle.Comment: Talk given at EPS2003 - Aachen, Germany, July 2003; 3 pages, no figure

Optical absorption and energy-loss spectra of aligned carbon nanotubes

Optical-absorption cross-sections and energy-loss spectra of aligned multishell carbon nanotubes are investigated, on the basis of photonic band-structure calculations. A local graphite-like dielectric tensor is assigned to every point of the tubules, and the effective transverse dielectric function of the composite is computed by solving Maxwell's equations in media with tensor-like dielectric functions. A Maxwell-Garnett-like approach appropriate to the case of infinitely long anisotropic tubules is also developed. Our full calculations indicate that the experimentally measured macroscopic dielectric function of carbon nanotube materials is the result of a strong electromagnetic coupling between the tubes. An analysis of the electric-field pattern associated with this coupling is presented, showing that in the close-packed regime the incident radiation excites a very localized tangential surface plasmon.Comment: 7 pages, 12 figures, to appear in Eur. Phys. J.

Real-time support for high performance aircraft operation

The feasibility of real-time processing schemes using artificial neural networks (ANNs) is investigated. A rationale for digital neural nets is presented and a general processor architecture for control applications is illustrated. Research results on ANN structures for real-time applications are given. Research results on ANN algorithms for real-time control are also shown

Variational Monte Carlo with the Multi-Scale Entanglement Renormalization Ansatz

Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the multi-scale entanglement renormalization ansatz (MERA), which is a unitary tensor network. Two major adjustments are required compared to previous proposals with non-unitary tensor networks. First, instead of sampling over configurations of the original lattice, made of L sites, we sample over configurations of an effective lattice, which is made of just log(L) sites. Second, the optimization of unitary tensors must account for their unitary character while being robust to statistical noise, which we accomplish with a modified steepest descent method within the set of unitary tensors. We demonstrate the performance of the variational Monte Carlo MERA approach in the relatively simple context of a finite quantum spin chain at criticality, and discuss future, more challenging applications, including two dimensional systems.Comment: 11 pages, 12 figures, a variety of minor clarifications and correction

On the charge radius of the neutrino

Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process-independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $WW$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective WW box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target-fermions are right-handedly polarized. In this way we obtain a unique decomposition of effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. We elaborate on the tree-level origin of the mechanism which enforces at one-loop level massive cancellations among the longitudinal momenta appearing in the Feynman diagrams, and in particular those associated with the non-abelian character of the theory. Various issues related to the known connection between the pinch technique and the Background Field Method are further clarified. Explicit closed expressions for the neutrino charge radius are reported.Comment: 26 pages, plain Latex, 7 Figures in a separate ps fil

A generalization of Bohr's Equivalence Theorem

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In fact, the main result of this paper consists of a result like Bohr's equivalence theorem extended to the case of these functions.Comment: Because of a mistake detected in one of the references, the previous version of this paper has been modified by the authors to restrict the scope of its application to the case of existence of an integral basi