Relaxation of classical many-body Hamiltonians in one dimension

The relaxation of Fourier modes of Hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wave number of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.