73 research outputs found
Asymmetric Unimodal Maps: Some Results from q-generalized Bit Cumulants
In this study, using q-generalized bit cumulants (q is the nonextensivity
parameter of the recently introduced Tsallis statistics), we investigate the
asymmetric unimodal maps. The study of the q-generalized second cumulant of
these maps allows us to determine, for the first time, the dependence of the
inflexion paremeter pairs (z_1,z_2) to the nonextensivity parameter q. This
behaviour is found to be very similar to that of the logistic-like maps
(z_1=z_2=z) reported recently by Costa et al. [Phys.Rev.E 56 (1997) 245].Comment: 6 pages with 3 fig
Generalized Huberman-Rudnick scaling law and robustness of -Gaussian probability distributions
We generalize Huberman-Rudnick universal scaling law for all periodic windows
of the logistic map and show the robustness of -Gaussian probability
distributions in the vicinity of chaos threshold. Our scaling relation is
universal for the self-similar windows of the map which exhibit period-doubling
subharmonic bifurcations. Using this generalized scaling argument, for all
periodic windows, as chaos threshold is approached, a developing convergence to
-Gaussian is numerically obtained both in the central regions and tails of
the probability distributions of sums of iterates.Comment: 13 pages, 3 figure
Mixing and relaxation dynamics of the Henon map at the edge of chaos
The mixing properties (or sensitivity to initial conditions) and relaxation
dynamics of the Henon map, together with the connection between these concepts,
have been explored numerically at the edge of chaos. It is found that the
results are consistent with those coming from one-dimensional dissipative maps.
This constitutes the first verification of the scenario in two-dimensional
cases and obviously reinforces the idea of weak mixing and weak chaos.
Keywords: Nonextensive thermostatistics, Henon map, dynamical systemsComment: 10 pages with 3 fig
Dissipative maps at the chaos threshold: Numerical results for the single-site map
We numerically study, at the edge of chaos, the behaviour of the sibgle-site
map , where is the map parameter.Comment: 8 pages with 4 figures, submitted to Physica
Exact and approximate results of non-extensive quantum statistics
We develop an analytical technique to derive explicit forms of
thermodynamical quantities within the asymptotic approach to non-extensive
quantum distribution functions. Using it, we find an expression for the number
of particles in a boson system which we compare with other approximate scheme
(i.e. factorization approach), and with the recently obtained exact result. To
do this, we investigate the predictions on Bose-Einstein condensation and the
blackbody radiation. We find that both approximation techniques give results
similar to (up to ) the exact ones, making them a useful tool
for computations. Because of the simplicity of the factorization approach
formulae, it appears that this is the easiest way to handle with physical
systems which might exhibit slight deviations from extensivity.Comment: 15 pages, prl revtex style, 4 ps figures. New -shortened- version
accepted for publication in Eur. Phys. J.
The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics
As well known, Boltzmann-Gibbs statistics is the correct way of
thermostatistically approaching ergodic systems. On the other hand, nontrivial
ergodicity breakdown and strong correlations typically drag the system into
out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide
class of such systems, it has been shown in recent years that the correct
approach is to use Tsallis statistics instead. Here we show how the dynamics of
the paradigmatic conservative (area-preserving) standard map exhibits, in an
exceptionally clear manner, the crossing from one statistics to the other. Our
results unambiguously illustrate the domains of validity of both
Boltzmann-Gibbs and Tsallis statistics
Generalized quantal distribution functions within factorization approach: Some general results for bosons and fermions
The generalized quantal distribution functions are investigated concerning
systems of non-interacting bosons and fermions. The formulae for the number of
particles and energy are presented and applications to the Chandrasekhar limit
of white dwarfs stars and to the Bose-Einstein condensation are commented.Comment: 10 pages, prl revtex style, 2 ps figure
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