Physical consequences of complex dimensions of fractals
Physical consequences of complex dimensions of fractals
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DOI：
10.1209/0295-5075/88/40007
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发表时间：
2009-11-01
期刊：
影响因子：
1.8
通讯作者：
Teplyaev, A.
中科院分区：
文献类型：
--
作者：
Akkermans, E.;Dunne, G. V.;Teplyaev, A.
人们已经认识到，分形的特征可能是复杂的维度，由相应 zeta 函数的复杂极点产生，我们在这里表明，这些会导致各种物理量的振荡行为。我们将这些复杂极点的物理起源确定为拉普拉斯迭代特征值的指数大简并性，并讨论了在量子介观系统中的应用，例如能级数涨落 Sigma(2)(E) 中的振荡，作为对随机矩阵理论中获得的结果的校正。我们为钻石分形族的这些振荡提出了明确的表达式，也将其作为分层晶格进行研究。版权所有 (C) EPLA，2009
It has been realized that fractals may be characterized by complex dimensions, arising from complex poles of the corresponding zeta function, and we show here that these lead to oscillatory behavior in various physical quantities. We identify the physical origin of these complex poles as the exponentially large degeneracy of the iterated eigenvalues of the Laplacian, and discuss applications in quantum mesoscopic systems such as oscillations in the fluctuation Sigma(2)(E) of the number of levels, as a correction to results obtained in random matrix theory. We present explicit expressions for these oscillations for families of diamond fractals, also studied as hierarchical lattices. Copyright (C) EPLA, 2009