Long-Time Behavior of the Vibration in One-Dimensional Harmonic Lattice

This is the authors' abstract. We don't add key points for this paper.

A study is made of the vibration in one-dimensional system of identical particles which are held together by harmonic forces. The long-time averages of mechanical quantities, especially, of the kinetic energy and the potential energy of the system are discussed in the case when a constant external force is applied to one of the particles. As far as the velocity of a particle is concerned, the Maxwellian distribution is established. However some, correlations between the velocities of neighboring particles remain unvanished. This means that the system does not reach to the true thermal equilibrium.