The paper investigates the notion of outage, as an assessment of the likelihood of a bit being in error, for chaos-based communication systems. It is seen as a complementary measure of performance to bit error rate. For antipodal chaos shift keying (CSK) a theoretically exact formula is derived which is then used in specific cases to obtain useful qualitative and quantitative information. Illus...

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term cr...

We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature chaos. To this end, we combine the replica Bethe Ansatz approach outlined by Sales and Yoshino (e-print cond-mat/0112384), the mapping to a modified Sinai model, and numerically exact calcu...

Polynomial maps offer analytical properties used to obtain better performances in the scope of chaos synchronization under noisy channels. This paper presents a new method to simplify equations of the Exact Polynomial Kalman Filter (ExPKF) given in [1]. This faster algorithm is compared to other estimators showing that performances of all considered observers vanish rapidly with the channel noi...

A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm...

We present in this note an alternative yet simple approach to obtain the Devaney-Nitecki horseshoe region for the Hénon maps. Our approach is based on the anti-integrable limit and the implicit function theorem. We also highlight an application to the logistic maps.

We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest-neighbor hopping and interaction, and next-nearest-neighbor interaction. The latter breaks...

Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and specially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance...

We discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. These results have been possible due to connections shown between random matrix models, many-body theories, and dynamical systems. We believe that these results and connections will pave the way to a better understanding of quantum chaos.