Long time scale in Hamiltonian systems with internal degrees of freedom: Numerical study of a diatomic gas
We performed molecular dynamics simulations on a one-dimensional diatomic gas to investigate the possible long time scale inherent in heterogeneous Hamiltonian systems. The exponentially long time scale for energy sharing between the translational motion and the vibrational one certainly exists in a large limit of the system size. The time scale depends on the vibrational frequency $\omega$ not as in the pure exponential form $\sim \exp[B\omega]$ but as $\sim \exp[B\omega^{\alpha}]$ with $\alpha<1$, in good agreement with the expression derived from the Landau-Teller approximation. The numerical simulations show that the complete resonance condition for vibrational frequencies assumed in the analytical treatment is not essential for the long time scale. Some discussions of $1/f$ fluctuations based on the present results will be given.