Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

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

2010-09-15

arxiv.org/abs/1009.3049v2

Nonlinear Sciences

Chaotic Dynamics

32 pages, 13 figures, Submitted for publication to Physica A

Scientific paper

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

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