### Abstract

In the present work we study the Fermi-Pasta-Ulam (FPU) β-model involving long-range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents α1 and α2 respectively, which make the forces decay with distance r. Our results demonstrate that weak chaos, in the sense of decreasing Lyapunov exponents, and q-Gaussian probability density functions (pdfs) of sums of the momenta, occurs only when long-range interactions are included in the quartic part. More importantly, for 0 ≤ α_{2}<1, we obtain extrapolated values for q≡q∞<1, as N→∞, suggesting that these pdfs persist in that limit. On the other hand, when long-range interactions are imposed only on the quadratic part, strong chaos and purely Gaussian pdfs are always obtained for the momenta. We have also focused on similar pdfs for the particle energies and have obtained qE-exponentials (with qE < 1) when the quartic-term interactions are long-ranged, otherwise we get the standard Boltzmann-Gibbs weight, with q = 1. The values of qE coincide, within small discrepancies, with the values of q obtained by the momentum distributions.

Original language | English |
---|---|

Article number | 123206 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2016 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 22 2016 |

Externally published | Yes |

### Fingerprint

### Keywords

- metastable states
- nonlinear dynamics
- numerical simulations
- thermalization

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2016*(12), [123206]. https://doi.org/10.1088/1742-5468/aa4f0e

**Dynamics and statistics of the Fermi-Pasta-Ulam β-model with different ranges of particle interactions.** / Christodoulidi, Helen; Bountis, Tassos; Tsallis, Constantino; Drossos, Lambros.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2016, no. 12, 123206. https://doi.org/10.1088/1742-5468/aa4f0e

}

TY - JOUR

T1 - Dynamics and statistics of the Fermi-Pasta-Ulam β-model with different ranges of particle interactions

AU - Christodoulidi, Helen

AU - Bountis, Tassos

AU - Tsallis, Constantino

AU - Drossos, Lambros

PY - 2016/12/22

Y1 - 2016/12/22

N2 - In the present work we study the Fermi-Pasta-Ulam (FPU) β-model involving long-range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents α1 and α2 respectively, which make the forces decay with distance r. Our results demonstrate that weak chaos, in the sense of decreasing Lyapunov exponents, and q-Gaussian probability density functions (pdfs) of sums of the momenta, occurs only when long-range interactions are included in the quartic part. More importantly, for 0 ≤ α2<1, we obtain extrapolated values for q≡q∞<1, as N→∞, suggesting that these pdfs persist in that limit. On the other hand, when long-range interactions are imposed only on the quadratic part, strong chaos and purely Gaussian pdfs are always obtained for the momenta. We have also focused on similar pdfs for the particle energies and have obtained qE-exponentials (with qE < 1) when the quartic-term interactions are long-ranged, otherwise we get the standard Boltzmann-Gibbs weight, with q = 1. The values of qE coincide, within small discrepancies, with the values of q obtained by the momentum distributions.

AB - In the present work we study the Fermi-Pasta-Ulam (FPU) β-model involving long-range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents α1 and α2 respectively, which make the forces decay with distance r. Our results demonstrate that weak chaos, in the sense of decreasing Lyapunov exponents, and q-Gaussian probability density functions (pdfs) of sums of the momenta, occurs only when long-range interactions are included in the quartic part. More importantly, for 0 ≤ α2<1, we obtain extrapolated values for q≡q∞<1, as N→∞, suggesting that these pdfs persist in that limit. On the other hand, when long-range interactions are imposed only on the quadratic part, strong chaos and purely Gaussian pdfs are always obtained for the momenta. We have also focused on similar pdfs for the particle energies and have obtained qE-exponentials (with qE < 1) when the quartic-term interactions are long-ranged, otherwise we get the standard Boltzmann-Gibbs weight, with q = 1. The values of qE coincide, within small discrepancies, with the values of q obtained by the momentum distributions.

KW - metastable states

KW - nonlinear dynamics

KW - numerical simulations

KW - thermalization

UR - http://www.scopus.com/inward/record.url?scp=85008420079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85008420079&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aa4f0e

DO - 10.1088/1742-5468/aa4f0e

M3 - Article

VL - 2016

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 12

M1 - 123206

ER -