15 research outputs found
Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
We present a molecular dynamics test of the Central Limit Theorem (CLT) in a
paradigmatic long-range-interacting many-body classical Hamiltonian system, the
HMF model. We calculate sums of velocities at equidistant times along
deterministic trajectories for different sizes and energy densities. We show
that, when the system is in a chaotic regime (specifically, at thermal
equilibrium), ergodicity is essentially verified, and the Pdfs of the sums
appear to be Gaussians, consistently with the standard CLT. When the system is,
instead, only weakly chaotic (specifically, along longstanding metastable
Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time
averages) is observed, and robust -Gaussian attractors emerge, consistently
with recently proved generalizations of the CLT.Comment: 6 pages 7 figures. Improved version accepted for publication on
Europhysics Letter
On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al
In the present paper we refute the criticism advanced in a recent preprint by
Figueiredo et al [1] about the possible application of the -generalized
Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body
classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model.
We exhibit that, contrary to what is claimed by these authors and in accordance
with our previous results, -Gaussian-like curves are possible and real
attractors for a certain class of initial conditions, namely the one which
produces nontrivial longstanding quasi-stationary states before the arrival,
only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for
publication in Europhysics Letters, (2009) in pres
Noise, Synchrony and Correlations at the Edge of Chaos
We study the effect of a weak random additive noise in a linear chain of N
locally-coupled logistic maps at the edge of chaos. Maps tend to synchronize
for a strong enough coupling, but if a weak noise is added, very intermittent
fluctuations in the returns time series are observed. This intermittency tends
to disappear when noise is increased. Considering the pdfs of the returns, we
observe the emergence of fat tails which can be satisfactorily reproduced by
-Gaussians curves typical of nonextensive statistical mechanics.
Interoccurrence times of these extreme events are also studied in detail.
Similarities with recent analysis of financial data are also discussed.Comment: 6 pages, 8 figures, new figure added - Version accepted for
publication in Physical Review
Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks
Using numerical modeling we study emergence of structure and
structure-related nonlinear conduction properties in the self-assembled
nanoparticle films. Particularly, we show how different nanoparticle networks
emerge within assembly processes with molecular bio-recognition binding. We
then simulate the charge transport under voltage bias via single-electron
tunnelings through the junctions between nanoparticles on such type of
networks. We show how the regular nanoparticle array and topologically
inhomogeneous nanonetworks affect the charge transport. We find long-range
correlations in the time series of charge fluctuation at individual
nanoparticles and of flow along the junctions within the network. These
correlations explain the occurrence of a large nonlinearity in the simulated
and experimentally measured current-voltage characteristics and non-Gaussian
fluctuations of the current at the electrode.Comment: 10 pages, 7 figure
Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions
In this letter we discuss the validity of the ergodicity hypothesis in
theories of violent relaxation in long-range interacting systems. We base our
reasoning on the Hamiltonian Mean Field model and show that the life-time of
quasi-stationary states resulting from the violent relaxation does not allow
the system to reach a complete mixed state. We also discuss the applicability
of a generalization of the central limit theorem. In this context, we show that
no attractor exists in distribution space for the sum of velocities of a
particle other than the Gaussian distribution. The long-range nature of the
interaction leads in fact to a new instance of sluggish convergence to a
Gaussian distribution.Comment: 13 pages,6 figure