422 research outputs found
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
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 of
one-sided L\'evy stable distributions with rational index , with
. 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 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 and . We
present a fast and accurate numerical scheme, based on an early integral
representation due to Mikusinski, for the evaluation of and
, their cumulative distribution function and their derivatives
for any real index . 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 . We
show that and 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
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
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