Wavelets and multifractality: Application to Anderson localized wave functions
Institut für Theoretische Physik III,
Justus-Liebig-Universität, 35392 Giessen, Germany
2 Institut für Theoretische Physik, Technische Universität - 01062 Dresden, Germany
Accepted: 12 August 1996
We discuss a simple method for analysing the local scaling behavior of the fluctuations of random probability distributions. The usefulness of the method, based on a discrete wavelet approach, is illustrated for the case of Anderson localized wave functions, , in one dimension, for which the standard multifractal analysis has led to controversial conclusions. The method suggests that is not multifractal in space and has similar statistical properties as profiles generated by simple random walks in one dimension.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 63.20.Pw – Localized modes
© EDP Sciences, 1996