MULTIFRACTAL PROPERTIES OF THE STRUCTURE FACTOR OF A CLASS OF SUBSTITUTIONAL SEQUENCES

被引:11
作者
CHENG, ZM [1 ]
SAVIT, R [1 ]
机构
[1] UNIV MICHIGAN, DEPT PHYS, ANN ARBOR, MI 48109 USA
来源
PHYSICAL REVIEW A | 1991年 / 44卷 / 10期
关键词
D O I
10.1103/PhysRevA.44.6379
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We show how to estimate the multifractal generating functional of the structure factor of a class of substitutional sequences. These sequences are sequences of two elements, a and b, and are generated by the repetitive application of the rules a --> sigma-1(a,b) and b --> sigma-2(a,b), with the sigma's consisting of strings of a's and b's. We restrict ourselves to the case in which sigma-1 and sigma-2 each contain R elements. This set includes the case of the Thue-Morse sequence. Subject to a technical assumption, we present a systematic approximation scheme for the multifractal generating functional, in which the lowest-order approximation is the generating functional of an R-scale Cantor set. As a by-product of our analysis, we demonstrate the existence of a discontinuity in the multifractal spectrum of the Thue-Morse sequence, and explain the origin of that discontinuity. We present explicit results for two examples, including the Thue-Morse case, and compare the results of our approximations for the Thue-Morse system with numerical simulations.
引用
收藏
页码:6379 / 6385
页数:7
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