Fluctuations of the inverse participation ratio at the anderson transition

Abstract

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic “tail.” This scale invariance implies that the fractal dimensions Dq are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility χ is violated in the regime of strong multifractality, with χ → 1 in the limit D2 → 0. © 2000 The American Physical Society.