Antal T, Droz M, Györgyi G, Rácz Z
Département de Physique Théorique, Université de Genève, CH 1211 Genève 4, Switzerland.
Phys Rev Lett. 2001 Dec 10;87(24):240601. doi: 10.1103/PhysRevLett.87.240601. Epub 2001 Nov 19.
We study finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions, the Fisher-Tippett-Gumbel (FTG) distribution, emerges as the scaling function when boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the FTG distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.
我们研究了显示高斯1/f功率谱的系统中信号粗糙度的有限尺寸缩放。结果发现，当边界条件为周期性时，一种极值分布，即费舍尔-蒂皮特-贡贝尔（FTG）分布，作为缩放函数出现。我们提供了一个周期性1/f噪声的实际例子，并通过模拟证明，对于非周期性边界条件的情况，FTG分布也是一个很好的近似。对砷化镓薄膜中的电压波动进行了实验分析，发现与理论结果吻合良好。
