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We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {em one} disordered system experience strong level-to-level fluctuations in a wide energy range. The fluctuations grow substantially with increasing size of the system. We argue that the fluctuations of the correlation dimension, $D_2$ of the wave functions are the main reason for this. The distribution of these correlation dimensions at the transition is calculated. In the thermodynamic limit ($Lto infty$) it does not depend on the system size $L$. An interesting feature of this limiting distribution is that it vanishes exactly at $D_{rm 2max}=1.83$, the highest possible value of the correlation dimension at the Anderson threshold in this model.
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to i
The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is found, while
We consider the orthogonality catastrophe at the Anderson Metal-Insulator transition (AMIT). The typical overlap $F$ between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the A
We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes i
We describe a new multifractal finite size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simula