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 ≤ 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.
| 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 |
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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
Dynamics and statistics of the Fermi-Pasta-Ulam β-model with different ranges of particle interactions. / Christodoulidi, Helen; Bountis, Tassos; Tsallis, Constantino; Drossos, Lambros.
In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, No. 12, 123206, 22.12.2016.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:85008420079
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 -