RECONSTRUCTION OF SPECTRAL DENSITIES OF ANHARMONIC PHONONS FROM THEIRMOMENTS VIA THE EFFECTIVE-POTENTIAL METHOD AND THE CONTINUED-FRACTIONAPPROACH

We describe a method for determining the phonon spectral densities of three-dimensional quantum anharmonic crystals. The reconstruction of t he frequency dependence of the spectral densities is carried out by me ans of the evaluation of their frequency moments and the use of the co ntinued fraction approach. The first few frequency moments are calcula ted 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 expans ion is then terminated in both regimes by the use of a fitting of the classical molecular dynamics data. Advantages, limitations, and the re liability of this procedure are extensively discussed. Numerical resul ts are reported for a Lennard-Jones crystal modeling solid argon and k rypton. The temperature dependence and the relevance of quantum effect s on the line shapes are investigated for wave vectors at high-symmetr y points on the boundary of the first Brillouin zone of the reciprocal lattice.