Chaos around the superposition of a monopole and a thick disk

We extend recent investigations on the integrability of oblique orbits of test particles under the gravitational field corresponding to the superposition of an infinitesimally thin disk and a monopole to the more realistic case, for astrophysical purposes, of a thick disk. Exhaustive numerical analyses were performed and the robustness of the recent results is confirmed. We also found that, for smooth distributions of matter, the disk thickness can attenuate the chaotic behavior of the bounded oblique orbits. Perturbations leading to the breakdown of the reflection symmetry about the equatorial plane, nevertheless, may enhance significantly the chaotic behavior, in agreement with recent studies on oblate models.Comment: 11 pages, 4 figure

New no-scalar-hair theorem for black-holes

A new no-hair theorem is formulated which rules out a very large class of non-minimally coupled finite scalar dressing of an asymptotically flat, static, and spherically symmetric black-hole. The proof is very simple and based in a covariant method for generating solutions for non-minimally coupled scalar fields starting from the minimally coupled case. Such method generalizes the Bekenstein method for conformal coupling and other recent ones. We also discuss the role of the finiteness assumption for the scalar field.Comment: Revtex, 12 page

Ergodic transitions in continuous-time random walks

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes. On the other hand, for the case of non-identical trapping time densities over the lattice points, the distribution of time-averaged observables reveals that such systems are typically nonergodic, in agreement with some recent experimental evidences on the statistics of blinking quantum dots. Some explicit examples are considered in detail. Our results are independent of the lattice topology and dimensionality.Comment: 8 pages, final version to appear in PR

Non-Gaussian features of chaotic Hamiltonian transport

Some non-Gaussian aspects of chaotic transport are investigated for a general class of two-dimensional area-preserving maps. Kurtosis, in particular, is calculated from the diffusion and the Burnett coefficients, which are obtained analytically. A characteristic time scale delimiting the onset of the Markovian regime for the master equation is established. Some explicit examples are discussed.Comment: 19 pages, 6 Figures. v2: Grammatical corrections, new reference

Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions

We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\alpha(x)$ of one-sided L\'evy stable distributions with rational index $\alpha=l/k$, with $0<\alpha<1$. Since one-sided L\'evy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions $\rho_\alpha(x)$ of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of $l$ and $k$. We present a fast and accurate numerical scheme, based on an early integral representation due to Mikusinski, for the evaluation of $g_\alpha(x)$ and $\rho_\alpha(x)$, their cumulative distribution function and their derivatives for any real index $\alpha\in (0,1)$. As an application, we explore some properties of these probability density functions. In particular, we determine the location and value of their maxima as functions of the index $\alpha$. We show that $\alpha \approx 0.567$ and $\alpha \approx 0.605$ correspond, respectively, to the one-sided L\'evy and Mittag-Leffler distributions with shortest maxima. We close by discussing how our results can elucidate some recently described dynamical behavior of intermittent systems.Comment: 6 pages, 5 figures. New references added, final version to appear in PRE. Numerical code available at http://vigo.ime.unicamp.br/dist