Compression and diffusion: a joint approach to detect complexity

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.Comment: 27 pages, 9 figure

Low Energy Solutions for the Semiclassical Limit of Schrodinger–Maxwell Systems

We show that the number of positive solutions of Schrodinger– Maxwell system on a smooth bounded domain depends on the topological properties of the domain. In particular we consider the Lusternik– Schnirelmann category and the Poincaré polynomial of the domain

Stable standing waves for a class of nonlinear Schroedinger-Poisson equations

We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0 \text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in \{8/3\}\cup (3,10/3)$. In the case $3<p<10/3$ we prove the existence and stability only for sufficiently large $L^2$-norm. In case $p=8/3$ our approach recovers the result of Sanchez and Soler \cite{SS} %concerning the existence and stability for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In a final section a further application to the Schr\"odinger equation involving the biharmonic operator is given

The tale of two centres

We study motion in the field of two fixed centres described by a family of Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change

Global compactness for a class of quasi-linear elliptic problems

We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.Comment: 19 page

Self-Configuring Silicon-Photonic Receiver for Multimode Free Space Channels

A self-configuring mesh of silicon Mach-Zehnder Interferometers is employed to receive two spatially overlapped orthogonal beams modulated at 10 Gbit/s. These beams, sharing the same wavelength and state of polarization, are separated with more than 30 dB isolation, and sorted out with no signal degradation

Location of the Energy Levels of the Rare-Earth Ion in BaF2 and CdF2

The location of the energy levels of rare-earth (RE) elements in the energy band diagram of BaF2 and CdF2 crystals is determined. The role of RE3+ and RE2+ ions in the capture of charge carriers, luminescence, and the formation of radiation defects is evaluated. It is shown that the substantial difference in the luminescence properties of BaF2:RE and CdF2:RE is associated with the location of the excited energy levels in the band diagram of the crystals

Multimode Free Space Optical Link Enabled by SiP Integrated Meshes

A silicon photonic mesh of tuneable Mach-Zehnder Interferometers (MZIs) is employed to receive two spatially-overlapped Hermite-Gaussian beams modulated at 10 Gbit/s, sharing the same wavelength and state of polarization. The mesh automatically self-configures, separating and sorting the two beams out without any excess loss