Energy Oscillations in a One-Dimensional Crystal

A study was conducted to consider and find an analytical solution to the problem of oscillations of the kinetic and potential energies in a one-dimensional crystal. An analytical solution for the linear interaction of particles, random initial velocities, and zero initial displacements was derived. It was shown that the time dependence of energies was expressed by the Bessel function, and the period and the damping rate of oscillations were determined. It was observed that the damping of energy oscillations was associated with the fact that correlations associating the motion of remote particles were excited. A method for the analytical description of such energy oscillations was proposed, which gave an exact solution of the corresponding mathematical problem along with performing a comparison with the results of numerical modeling.