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期刊论文

Multifractality of probability measure on energy-spectrum supports

杨展如Z.R. Yang

PHYSICAL REVIEW E VOLUME 47, NUMBER 2 FEBRUARY 1993,-0001,():

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摘要/描述

We have studied quadric type energy (frequency) recursion relations resulting from fractal lattices. We found that the allowed energy intervals in successive levels form two similar two-scale Cantor sets. If WE imagine the iterating procedure as a dynamical process, the iterating results in different levels gen-erate a"time"sequence, and we can introduce an equal probability measure Pu on a Cantor set and con-struct,following Helsey et a1. [Phys. Rev. A 33, 1141 (1986)], a partition function F (q,T) =∑ipq/17; finally, we obtain Dq-q and f (a)-a curves. A number of exactly soluable examples are investigated.

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