STATISTICAL BEHAVIOR OF CHARACTERISTIC LENGTHS OF VIBRATIONS ON TWO-DIMENSIONAL RANDOM FRACTALS

Abstract

We analyze the behavior of some characteristic lengths of the normal modes of square percolating lattices at threshold. Generalized inverse participation ratios are taken as estimates of the localization lengths, while the wavenumber kM having the maximum weight in the Fourier transform of the autocorrelation function of each mode is supposed to be inversely proportional to the relevant wavelength. Both site and bond percolating lattices are considered. It is found that, on average, these quantities follow about the same supposed scaling law, therefore supporting the idea of a universal length. At the same time they all exhibit large deviations from the expected values with no apparent correlation among fluctuations in the localization lengths and in the relevant wavelengths, as it turns out from the computed correlation coefficient.