TY - JOUR
T1 - Multifractal localization
AU - Aharony, Amnon
AU - Harris, A. Brooks
N1 - Funding Information:
We would like to thank A. Bunde and S. Havlin for very useful discussions. This work has been supported by the Israel Academy of Sciences and Humanities, the U.S.-Israel Binational ScienceF oundation and the NSF under Grant No. DMR-91-22784.
PY - 1992/12/15
Y1 - 1992/12/15
N2 - We discuss scaling with many length scale exponents (multifractality) mainly in the context of localized excitations in a random (or fractal) environment. Many distributions of physical properties on percolating clusters may be quite sharp when expressed in terms of the chemical (shortest path) distance, but become very broad when expressed in terms of the real-space Euclidean displacement. In many cases this reasoning provides a simple physical picture of multifractality. Specifically, we discuss the distributions of localized wave functions on percolating clusters, on length scales larger than the localization length. For deep impurity states, we find multifractality with new crossover features. For states inside the band, for fractons and for random walks, the situation is more complicated and we analyze several recent relevant numerical studies.
AB - We discuss scaling with many length scale exponents (multifractality) mainly in the context of localized excitations in a random (or fractal) environment. Many distributions of physical properties on percolating clusters may be quite sharp when expressed in terms of the chemical (shortest path) distance, but become very broad when expressed in terms of the real-space Euclidean displacement. In many cases this reasoning provides a simple physical picture of multifractality. Specifically, we discuss the distributions of localized wave functions on percolating clusters, on length scales larger than the localization length. For deep impurity states, we find multifractality with new crossover features. For states inside the band, for fractons and for random walks, the situation is more complicated and we analyze several recent relevant numerical studies.
UR - http://www.scopus.com/inward/record.url?scp=0001757203&partnerID=8YFLogxK
U2 - 10.1016/0378-4371(92)90553-3
DO - 10.1016/0378-4371(92)90553-3
M3 - Article
AN - SCOPUS:0001757203
SN - 0378-4371
VL - 191
SP - 365
EP - 378
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1-4
ER -