Energy Oscillations in a One-Dimensional Crystal

摘要

Oscillations of the kinetic and potential energies in a one-dimensional crystal (the chain of particles) are considered. An analytical solution for the linear interaction of particles, random initial velocities, and zero initial displacements is derived. It is shown that the time dependence of energies is expressed by the Bessel function, and the period and the damping rate of oscillations are determined. Analytical conclusions are confirmed by computer modeling. According to the results found, in order to describe high-speed transient processes, apart from the consideration of velocities dispersion (which determines the temperature in the equilibrium statistical mechanics), the correlations of velocities of different particles should be considered. In particular, the damping of energy oscillations is associated with the fact that correlations associating the motion of remote particles are excited.