84,061 research outputs found
The rate of entropy increase at the edge of chaos
Under certain conditions, the rate of increase of the statistical entropy of
a simple, fully chaotic, conservative system is known to be given by a single
number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This
connection is here generalized to a simple dissipative system, the logistic
map, and especially to the chaos threshold of the latter, the edge of chaos. It
is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon
entropy is not appropriate. Instead, the non-extensive entropy , must be used. The latter contains a
parameter q, the entropic index which must be given a special value
(for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos
under consideration. The same q^* enters also in the description of the
sensitivity to initial conditions, as well as in that of the multifractal
spectrum of the attractor.Comment: 6 pages, Latex, 4 figures included, final version accepted for
publication in Physics Letters
Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos
We investigate the probability density of rescaled sum of iterates of
sine-circle map within quasi-periodic route to chaos. When the dynamical system
is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is
expected to be valid, but at the edge of chaos where iterates have strong
correlations, the standard CLT is not necessarily to be valid anymore. We
discuss here the main characteristics of the central limit behavior of
deterministic dynamical systems which exhibit quasi-periodic route to chaos. At
the golden-mean onset of chaos for the sine-circle map, we numerically verify
that the probability density appears to converge to a q-Gaussian with q<1 as
the golden mean value is approached.Comment: 7 pages, 7 figures, 1 tabl
Classical and quantum systems: transport due to rare events
We review possible mechanisms for energy transfer based on 'rare' or
'non-perturbative' effects, in physical systems that present a many-body
localized phenomenology. The main focus is on classical systems, with or
without quenched disorder. For non-quantum systems, the breakdown of
localization is usually not regarded as an issue, and we thus aim at
identifying the fastest channels for transport. Next, we contemplate the
possibility of applying the same mechanisms in quantum systems, including
disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized
systems with mobility edges at energies below the edge, and strongly disordered
lattice systems in . For quantum mechanical systems, the relevance of
these considerations for transport is currently a matter of debate.Comment: Review paper. To appear on the special issue on Many-body
Localization in Annalen der Physi
The (In)Stability of Planetary Systems
We present results of numerical simulations which examine the dynamical
stability of known planetary systems, a star with two or more planets. First we
vary the initial conditions of each system based on observational data. We then
determine regions of phase space which produce stable planetary configurations.
For each system we perform 1000 ~1 million year integrations. We examine
upsilon And, HD83443, GJ876, HD82943, 47UMa, HD168443, and the solar system
(SS). We find that the resonant systems, 2 planets in a first order mean motion
resonance, (HD82943 and GJ876) have very narrow zones of stability. The
interacting systems, not in first order resonance, but able to perturb each
other (upsilon And, 47UMa, and SS) have broad regions of stability. The
separated systems, 2 planets beyond 10:1 resonance, (we only examine HD83443
and HD168443) are fully stable. Furthermore we find that the best fits to the
interacting and resonant systems place them very close to unstable regions. The
boundary in phase space between stability and instability depends strongly on
the eccentricities, and (if applicable) the proximity of the system to perfect
resonance. In addition to million year integrations, we also examined stability
on ~100 million year timescales. For each system we ran ~10 long term
simulations, and find that the Keplerian fits to these systems all contain
configurations which may be regular on this timescale.Comment: 37 pages, 49 figures, 13 tables, submitted to Ap
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