# Multifractal analysis with the probability density function at the 3D Anderson transition

• Dr. Alberto Rodriguez, U of Warwick
• Thursday 15 October 2009, 14:00-15:00
• Theory Library.

The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum $f(\alpha)$ in which the role of finite-size corrections is properly analysed. We show the existence of a symmetry relation in the PDF . From the PDF , we extract information about the multifractal spectrum at criticality such as the presence of negative fractal dimensions. The critical exponents of the metal-insulator transition could also be obtained from the distribution of wavefunction amplitudes. A PDF -based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.

This talk is part of the Theoretical Physics Seminars series.