Spectral shapes of Lennard-Jones chains

We show how the results of classical molecular-dynamics simulations can 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 chain of N atoms interacting through a nearest-neighbor Lennard-Jones potential, can be calculated accurately in the following way. C(k,omega) is expressed in the form of a continued fraction, whose coefficients are given in terms of its even-frequency moments. The latter, up through the sixth, are calculated from an effective potential that includes the effects of quantum fluctuations. The continued fraction is then terminated by the use of a termination parameter that is determined from a fit of the same continued fraction to the spectral density calculated by means of a classical molecular-dynamics simulation.