Heat transfer in infinite harmonic one-dimensional crystals

A closed system of differential-difference equations describing thermal processes in one-dimensional harmonic crystals is obtained in the paper. An equation connecting the heat flow and the kinetic temperature is obtained as a solution of the system. The obtained law of heat conduction is different from Fourier's law and results in an equation that combines properties of the standard heat equation and the wave equation. The resulting equation is an analytic consequence from the dynamical equations for the particles in the crystal. Unlike equations of hyperbolic heat conduction, this equation is time-reversible and has only one independent parameter. A general analytical solution of this differential equations is obtained, and the analytical results are confirmed by computer simulations.