Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis

Details Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis

2005-02-28

arxiv.org/abs/nlin/0502064v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 5 figures, RevTeX4 PRE format; to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.71.046207

The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Results obtained in a previous work [M. Romero-Bastida, Phys. Rev. E {\bf69}, 056204 (2004)] suggest that the impurity does not contribute significantly to the dynamics of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. The ($r,\tau$) entropy, which measures the amount of information generated by unit time at different scales $\tau$ of time and $r$ of the observable, is numerically computed by methods of nonlinear time-series analysis using the position and momentum signals of the heavy impurity for various values of the energy density $\epsilon$ (energy per degree of freedom) of the system and some values of the impurity mass $M$. Results obtained from these two time series are compared and discussed.

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