2000/11/30 by E. Cuevas, V. Gasparian, M. Ortuno +1 · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.87.056601
published as Phys. Rev. Lett. 87, 056601 (2001) · RevTex, 4 pages, 4 eps figures. Final version to be published in Phys. Rev. Lett
arxiv created 2001/06/22 · openalex publication_date 2001/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.