Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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
1993

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},
    URL = {http://www.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://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2473.html
%F De Luca:M93/92