Time autocorrelation functions for harmonic solids from Gaussian quadratures

Gaussian quadratures determine time autocorrelation functions (TAF's) of harmonic solids from modified moments of the phonon density of states. The quadratures determine the TAF's with great precision out to times more than twice those at which the Taylor series expansion in time ceases to be accurate. The quadratures provide rigorous bounds to the TAF's over most of this range in time. Moreover, a single set of abscissas and weights determines the quadratures for both position and momentum TAF's. The method can determine TAF's to long times, so that the asymptotic behavior can be examined for a simple model solid.