Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a [Formula Presented] lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam β model). We take the initial energy to be either in a single mode γ or in a package of low-frequency modes centered at γ and of width δγ, with both γ and δγ proportional to N. These initial conditions both give, for finite energy densities [Formula Presented] 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 [Formula Presented] A theory of the scaling with [Formula Presented] is presented and compared to the numerical results in the range [Formula Presented]. © 1999 The American Physical Society.