Anomalously large critical regions in power-law random matrix ensembles

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...

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Bibliographic Details
Published in:Physical review letters 2001-07, Vol.87 (5), p.056601-056601, Article 056601
Main Authors: Cuevas, E, Gasparian, V, Ortuño, M
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
FRACTALS
GREEN FUNCTION
WAVE FUNCTIONS
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.87.056601