Approach to equilibrium in a chain of nonlinear oscillators

Overview & Synopsis

We consider the approach to thermodynamical equilibrium in a chain of coupled nonlinear oscillators when energy is initially fed only to the longest wavelength modes. Consideration of the effects of singularities in the complex plane of the solutions of the equations of motion allows us to predict that at not too long times the energy spectrum has an exponential tail in the wavenumber k and to distinguish between two time regions : a short time region where the slope of the exponential shows a linear dependence on In t, and an intermediate region where it is proportional to (In t)-1/2. These predictions are successfully compared with the numerical simulations we have performed on the system.