Finite times to equipartition in the thermodynamic limit

Details Finite times to equipartition in the thermodynamic limit Finite times to equipartition in the thermodynamic limit

1999-05-31

arxiv.org/abs/chao-dyn/9906005v1

Nonlinear Sciences

Chaotic Dynamics

Plain TeX, 5 `eps' figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.60.3781

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.

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