Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coup led 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 pack age of low-frequency modes centered at gamma and of width delta gamma, with both gamma and delta gamma proportional to N. These initial conditions bot h give, for finite energy densities E/N, a scaling in the thermodynamic lim it (large N), of a finite time to equipartition which is inversely proporti onal 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 nume rical results in the range 0.03 less than or equal to E/N less than or equa l to 0.8. [S1063-651X(99)09110-2].