Science. 1986 Feb 21;231(4740):814-9. doi: 10.1126/science.231.4740.814.
Random structures often exhibit fractal geometry, defined in terms of the mass scaling exponent, D, the fractal dimension. The vibrational dynamics of fractal networks are expressed in terms of the exponent d, the fracton dimensionality. The eigenstates on a fractal network are spatially localized for d less than or equal to 2. The implications of fractal geometry are discussed for thermal transport on fractal networks. The electron-fracton interaction is developed, with a brief outline given for the time dependence of the electronic relaxation on fractal networks. It is suggested that amorphous or glassy materials may exhibit fractal properties at short length scales or, equivalently, at high energies. The calculations of physical properties can be used to test the fractal character of the vibrational excitations in these materials.
随机结构通常表现出分形几何，这是根据质量标度指数 D 和分形维数来定义的。分形网络的振动动力学可以用指数 d 来表示，即分形维数。当 d 小于或等于 2 时，分形网络上的本征态在空间上是局域的。讨论了分形几何对分形网络上热输运的影响。发展了电子-分形子相互作用，并简要概述了分形网络上电子弛豫的时间依赖性。有人认为，非晶或玻璃材料在短尺度或等效的高能下可能表现出分形特性。物理性质的计算可用于检验这些材料中振动激发的分形特征。
