36
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### Abstract

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-$$\beta$$) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within "small size" phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to $$t\approx10^6$$) by a $$q$$-Gaussian ($$1<q<3$$) distribution and tend to a Gaussian ($$q=1$$) for longer times, as the orbits eventually enter into "large size" chaotic domains. However, in agreement with other studies, we find in certain cases that the $$q$$-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called "crossover" function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these $$q$$-Gaussian distributions to identify two energy regimes of "weak chaos"-one where the system melts and one where it transforms from liquid to a gas state-by observing where the $$q$$-index of the distribution increases significantly above the $$q=1$$ value of strong chaos.

### Most cited references23

• Record: found

### Ergodic theory of chaos and strange attractors

(1985)
Bookmark
• Record: found

### Construction of higher order symplectic integrators

(1990)
Bookmark
• Record: found

### Ergodic theory of differentiable dynamical systems

(1979)
Bookmark

### Author and article information

###### Journal
2010-09-15
2011-05-07
###### Article
10.1016/j.physa.2011.05.026
1009.3049
fd1cb91e-e7af-44e2-a335-7b44a6128b06

32 pages, 13 figures, Submitted for publication to Physica A
nlin.CD

Nonlinear & Complex systems
Nonlinear & Complex systems