ENERGY-FLUCTUATION RELAXATION TOWARDS EQUILIBRIUM IN AN INFINITE CHAIN OF ANHARMONIC-OSCILLATORS

This study tries to extend results observed in finite chains, like slowing-down effects and stretched-exponential decays, into the thermodynamic limit. An infinite chain of nonlinear oscillators is related to pairs of coupled anharmonic modes, where each mode is coupled to an infinite number of harmonic oscillators (thermal baths). For the model of the two coupled infinite chains, the analytical treatment leads very naturally to a "critical" energy below which slowing-down effects and stretched-exponential decays should appear. Also, the model yields a zero-energy threshold for the onset of energy sharing between modes, suggesting that chaos should set in for arbitrarily small energies of the Hamiltonian. The theory is confirmed by digital simulations. These results seem to support the phenomenology observed in models with finite degrees of freedom, suggesting that this behavior survives in the thermodynamic limit and it is perhaps a common feature of chains of coupled anharmonic oscillators.