THE SPECTRAL SHAPE OF NONLINEAR CHAINS - VALIDITY OF PERTURBATIVE ANDMOMENT APPROACHES

We test the range of validity of the perturbative approach for calcula ting the spectral shape of a one-dimensional Lennard-Jones chain. We r econstruct the spectral shape from its frequency moments through the u se of a continued fraction representation with truncation. The quantum moments for the Lennard-Jones potential are calculated by means of th e effective potential method. The classical frequency moments are calc ulated exactly for this potential and for the approximation to it obta ined by expanding it in powers of the deviations from the position of its minimum through terms of fourth order. The comparison with molecul ar dynamics results for the same potentials confirms the validity of t he continued fraction approach, and shows that the perturbative approa ch is valid only at very low temperatures.