Quantumlike short-time behavior of a classical crystal

We have performed a molecular-dynamics simulation of a face-centered-cubic Lennard-Jones crystal, and studied its relaxation toward equilibrium and its microcanonical equilibrium dynamics through the computation of the normal modes. At low temperature, the weak interaction among normal modes yields a very slow relaxation of the fluctuation of the kinetic energy; this requires a new formulation of the measure of the microcanonical specific heat at constant volume. This specific heat turns out to depend on the time of observation; for times of the order of 20 ps, its values are much nearer to the quantum ones than to the value 3R predicted by the classical Dulong and Petit law. For longer observation times, the classical specific heat progressively approaches 3R over most of the temperature range of the solid crystal, with the exception of the lowest temperature range, where it still drops to values close to zero. The time dependence of the specific heat of the crystal is similar to the behavior found in a supercooled liquid near the glass transition.