Energy equipartition starting from high-frequency modes in the Fermi-Pasta-Ulam beta oscillator chain

We study the approach to equipartition in the Fermi-Pasta-Ulam oscillator c hain with quartic nonlinearity Fermi-Pasta-Ulam-(beta system) starting from generic high-frequency-mode initial conditions. Typically 90% of the energ y is placed in one high-frequency mode, with 10% in adjacent modes. The mod e energy is found to distribute itself into first a number of localized str uctures which coalesce over time into a single localized structure, a chaot ic breather (CB). Over longer times the CB is found to break up, with energ y transferred to lower frequency modes which do not have the breather symme try. A transition with decreasing initial mode frequency is found such that the CB does not form, as expected from the loss of breather symmetry. The scaling of CB formation time with energy density, E/N, is found to be Tba(E /N)(-1), and the scaling of equipartition time found to be T(eq)proportiona l to(E/N)(-2). The scaling of T-eq can be predicted from an argument which postulates stochastic diffusion from high-frequency-mode chaotic beat oscil lations to the low-frequency modes. The theory also predicts that a miminum value of E/N exists below which T-eq should increase more rapidly with E/N than in the power law range, and this transition has been found numericall y.