TY - JOUR

T1 - Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

AU - Antonopoulos, Ch

AU - Bountis, T.

AU - Basios, V.

N1 - Funding Information:
We are grateful to the referees for their useful comments and remarks. We also thank C. Tsallis, P. Tempesta and G. Ruiz-Lopez of the Centro Brasileiro de Pesquisas Fisicas in Rio de Janeiro for fruitful discussions during the preparation of the paper. Ch. A. was partially supported by the PAI 2007 - 2011 “NOSY-Nonlinear Systems, Stochastic Processes and Statistical Mechanics” (FD 9024CU1341 ) contract of ULB and a grant from G.S.R.T., Greek Ministry of Education , for the project “Complex Matter”, awarded under the auspices of the ERA Complexity Network. V.B. acknowledges the support of the European Space Agency under contract No. ESA AO-2004-070 . T.B. is grateful for the hospitality of the Centro Brasileiro de Pesquisas Fisicas, in Rio de Janeiro, March 1–April 5, 2010 and the Max Planck Institute for the Physics of Complex Systems in Dresden, April 5–June 25, 2010, while work for this paper was carried out.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - 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-β) 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 ≈ 106) 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.

AB - 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-β) 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 ≈ 106) 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.

KW - ''Edge of chaos"

KW - Multi-dimensional Hamiltonian systems

KW - Nonextensive statistical mechanics

KW - Quasi-stationary states

KW - Weak chaos

KW - q-Gaussian distributions

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U2 - 10.1016/j.physa.2011.05.026

DO - 10.1016/j.physa.2011.05.026

M3 - Article

AN - SCOPUS:79961027323

VL - 390

SP - 3290

EP - 3307

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 20

ER -