Slow relaxation in heterogeneous Hamiltonian systems: Numerical study compared with Landau-Teller approximation

We performed numerical simulations on a one-dimensional diatomic gas to investigate the possible long time scale in Hamiltonian systems with internal degrees of freedom. In the limit of the large system size, the time scale for energy sharing between the translational motion and the vibrational one grows as ∼ exp [B ω^α] with the vibrational frequency ω where 0 < α < 1. Although the present results agree fairly well with the Landau-Teller approximation in which α = 0.4, we note a slight deviation of an optimized α from this value. We ascribe it to a non-Debye type dynamics by presenting 1 / f^β like spectra of energy fluctuations. The simulations show that the complete resonance condition for vibrational frequencies assumed in the analytical treatment is not essential for the long time scale.