Universal evolution to equipartition in oscillator chains

We determine a universal evolution and time scale T to equipartition in a one-dimensional lattice of N masses coupled by quartic nonlinear (hard) springs. We consider chains made of two types of masses randomly distributed, and of random masses between limiting values. The initial energy is put in a low-frequency mode of mode number gamma. T is found to be inversely proportional to the initial beat frequency between mode gamma and the neighboring modes. It is also proportional to a factor N In(N)/N-c(1/2) where N-c is a measure of the modes quartically coupled to mode gamma.