DYNAMIC AND SCATTERING PROPERTIES OF THE SIERPINSKI GASKET

The dynamic and scattering properties of the Sierpinski gasket are studied in systems up to as large as N = 2391 486 atoms (level = 13). using the spectral moments method. Two models, with scalar and vectorial forces, are developed. The effects of disorder are also investigated, The density of states on the scalar perfect Sierpinski gasket is found to be in agreement with previous results. For the vectorial perfect model, we find that the density of states exhibits self-similar properties. For the disordered systems, results show that the density of states exhibits two regimes. For the disordered vectorial model, the density of states is proportional to omega in the low-frequency regime. A cross-over is found. and on short length scales the density of states is proportional to omega(a). Determination of the correlation functions shows that, although the density of states follows the Debye law, the low-frequency region does not correspond to an acoustic regime, which is in agreement with the lack of translational invariance. A microscopic theory of the scattering of light by fractals is developed and comparisons with recent results obtained in Raman scattering measurements of silica aerogels are reported. The results confirm that, in the fracton regime. the Raman intensity behaves with a power law, with the value of the exponent depending on the scaling properties and the susceptibility derivatives.