Raman scattering from fractals: Simulation on large structures by the method of moments

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Abstract
We have employed the method of spectral moments to study the density of vibrational states and the Raman coupling coefficient of large two- and three-dimensional percolators at threshold and at higher concentration. We first discuss the overflow and underflow problems of the procedure that arise when, as in the present case, it is necessary to calculate a few thousand moments. Then we report on the numerical results; these show that different scattering mechanisms, all a priori equally probable in real systems, produce largely different coupling coefficients with different frequency dependence. Our results are compared with existing scaling theories of Raman scattering. The situation that emerges is complex; on the one hand, there is indication that the existing theory is not satisfactory; on the other hand, the simulations above threshold show that in this case the coupling coefficients have very little resemblance, if any, to the same quantities at threshold.
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