A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation. (C) 2008 Elsevier Inc. All rights reserved.

Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.