2000/01/08 by Ferdinand Evers, F. Evers, A. D. Mirlin · 274 citations
Mathematics · Physics and Astronomy · #Compressibility #Critical exponent #Eigenvalues and eigenvectors #Fractal #Geometry #Invariant (physics) #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Power law #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Random matrix #Scale invariance #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.84.3690
published in Physical Review Letters 84(16), 3690-3693 (American Physical Society) · 4 pages, 3 eps figures
arxiv created 2000/01/08 · openalex publication_date 2000/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 D(q) are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility chi is violated in the regime of strong multifractality, with chi-->1 in the limit D2-->0.