SPECTRAL SHAPES OF LENNARD-JONES CHAINS

We show how the results of classical molecular-dynamics simulations ca n be used to improve the calculation of quantum spectral densities of anharmonic crystals. In particular we show that the spectral density C (k,omega)) of the displacement correlation function for a quantum chai n of N atoms interacting through a nearest-neighbor Lennard-Jones pote ntial, can be calculated accurately in the following way. C(k,omega) i s expressed in the form of a continued fraction, whose coefficients ar e given in terms of its even-frequency moments. The latter, up through the sixth, are calculated from an effective potential that includes t he effects of quantum fluctuations. The continued fraction is then ter minated by the use of a termination parameter that is determined from a fit of the same continued fraction to the spectral density calculate d by means of a classical molecular-dynamics simulation.