The Cercignani Conjecture About a Classical Zero-Point Energy, and Its Confirmation for Ionic Crystals

A characteristic feature of Quantum Mechanics is that it predicts the existence of zero-point energy, i.e., of states with a nonvanishing kinetic energy at zero temperature. This is a fact that is experimentally verified and is considered to be inconceivable in a classical frame. In the year 1972 Carlo Cercignani advanced the idea that a classical zero-point energy may be conceived, if one understands the corresponding motions as characterized by being (in the terminology used at those times) of “ordered” rather than of “chaotic” type. Here we illustrate how the Cercignani idea is actually implemented for an ionic crystal model which was already shown to be of such a realistic character as to reproduce in a remarkably good way, in terms of the Newtonian trajectories of the ions, the experimental infrared spectra.