Spectral Properties of Fractal Surfaces

The first investigation of the spectral dimension d double bar of a deterministic fractal surface is presented. Somewhat unexpectedly, numerical results strongly suggest d double bar = 2 for a whole class of surfaces, enclosing space regions with ordinary volume dimension. This conclusion is also supported by scaling arguments based on a connection with processes of diffusion in the presence of hierarchical waiting times. The problem of diffusion on our surface is also compared with that of random chain conformations. Within the numerical uncertainties the two problems seem to be characterized by identical end-to-end distance exponents.