Superlocalization, correlations and random walks on fractals

Amnon Aharony; A. Brooks Harris

doi:10.1016/0378-4371(90)90313-H

Superlocalization, correlations and random walks on fractals

Amnon Aharony, A. Brooks Harris

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

Upper and lower bounds are found for the anomalous decay exponent a of localized wave functions and of various two-point correlation functions on typical fractal configurations. The decay of the "superlocalized" wave functions is used to evaluate the decay of the probability distribution of a random walk, which is then used to obtain a Flory-like expression for self-avoiding walks. Emphasis is placed on the differences between "typical" and average quantities.

Original language	English
Pages (from-to)	38-46
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	163
Issue number	1
DOIs	https://doi.org/10.1016/0378-4371(90)90313-H
State	Published - 1 Feb 1990
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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abstract = "Upper and lower bounds are found for the anomalous decay exponent a of localized wave functions and of various two-point correlation functions on typical fractal configurations. The decay of the {"}superlocalized{"} wave functions is used to evaluate the decay of the probability distribution of a random walk, which is then used to obtain a Flory-like expression for self-avoiding walks. Emphasis is placed on the differences between {"}typical{"} and average quantities.",

author = "Amnon Aharony and {Brooks Harris}, A.",

note = "Funding Information: Work at Tel Aviv was supportedb y grantsf rom the U.S.-Israel Binational ScienceF oundation and from the Israel Academy of Sciencesa nd Humanities. Work at the University of Pennsylvaniaw as supportedb y the NSF under grant DMR 8520272.W ork at the University of Oslo was supportedb y VISTA, a researchc ooperationb etweent he NorwegianA cademy of Sciencea nd Letters and STATOIL, and by the Norwegian Council of Science and Humanities (NAVF).",

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AU - Brooks Harris, A.

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N2 - Upper and lower bounds are found for the anomalous decay exponent a of localized wave functions and of various two-point correlation functions on typical fractal configurations. The decay of the "superlocalized" wave functions is used to evaluate the decay of the probability distribution of a random walk, which is then used to obtain a Flory-like expression for self-avoiding walks. Emphasis is placed on the differences between "typical" and average quantities.

AB - Upper and lower bounds are found for the anomalous decay exponent a of localized wave functions and of various two-point correlation functions on typical fractal configurations. The decay of the "superlocalized" wave functions is used to evaluate the decay of the probability distribution of a random walk, which is then used to obtain a Flory-like expression for self-avoiding walks. Emphasis is placed on the differences between "typical" and average quantities.

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Superlocalization, correlations and random walks on fractals

Abstract

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