Reconstruction of spectral densities of anharmonic phonons from their moments via the effective-potential method and the continued-fraction approach

We describe a method for determining the phonon spectral densities of three-dimensional quantum anharmonic crystals. The reconstruction of the frequency dependence of the spectral densities is carried out by means of the evaluation of their frequency moments and the use of the continued fraction approach. The first few frequency moments are calculated in both classical (up to the sixth) and quantum regimes (up to the fourth) by resorting , respectively, to the Monte Carlo method and the effective potential Monte Carlo method. The continued fraction expansion is then terminated in both regimes by the use of a fitting of the classical molecular dynamics data. Advantages, limitations, and the reliability of this procedure are extensively discussed. Numerical results are reported for a Lennard-Jones crystal modeling solid argon and krypton. The temperature dependence and the relevance of quantum effects on the line shapes are investigated for wave vectors at high-symmetry points on the boundary of the first Brillouin zone of the reciprocal lattice. {} 1996 The American Physical Society.