Time Scale to Ergodicity in the FPU System

J. De Luca, Allan J. Lichtenberg and Michael A. Lieberman

EECS Department
University of California, Berkeley
Technical Report No. UCB/ERL M93/92
November 1993

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/ERL-93-92.pdf

We study the approach to near-equipartition in an N-dimensional FPU Hamiltonian. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy, one can reach near-equipartition if one waits for a time proportional N2. Below this critical energy the time is exponentially long. We develop a theory to understand the time evolution and deformation of the actions of the oscillators based on a normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for near-equipartition, the time scale to near-equipartition and the deformation of the actions below equipartition, in qualitative agreement with the numerical results.

BibTeX citation:

@techreport{De Luca:M93/92,
    Author = {De Luca, J. and Lichtenberg, Allan J. and Lieberman, Michael A.},
    Title = {Time Scale to Ergodicity in the FPU System},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    Month = {Nov},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2473.html},
    Number = {UCB/ERL M93/92},
    Abstract = {We study the approach to near-equipartition in an N-dimensional FPU Hamiltonian.  We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes.  Our results indicate a transition where, above a critical energy, one can reach near-equipartition if one waits for a time proportional N2.  Below this critical energy the time is exponentially long.  We develop a theory to understand the time evolution and deformation of the actions of the oscillators based on a normal form treatment of the resonances among the oscillators.  Our theory predicts the critical energy for near-equipartition, the time scale to near-equipartition and the deformation of the actions below equipartition, in qualitative agreement with the numerical results.}
}

EndNote citation:

%0 Report
%A De Luca, J.
%A Lichtenberg, Allan J.
%A Lieberman, Michael A.
%T Time Scale to Ergodicity in the FPU System
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/ERL M93/92
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1993/2473.html
%F De Luca:M93/92