摘要翻译：
导出了复杂随机态极值强度统计量的精确解析描述。这些态具有随机矩阵理论的高斯和圆形么正系综本征态的统计性质。尽管各分量通过归一化约束相关，但仍可导出维数N的所有值的紧凑公式。即使变量有界，最大强度结果也缓慢地接近Gumbel分布，而最小强度结果迅速地接近Weibull分布。由于随机矩阵理论可以应用于混沌量子系统，我们计算了标准映射的极值本征函数统计量，当其经典映射为完全混沌时，该标准映射具有参数。统计行为与有限n公式一致。
---
英文标题：
《Extreme statistics of complex random and quantum chaotic states》
---
作者：
Arul Lakshminarayan, Steven Tomsovic, Oriol Bohigas, Satya N. Majumdar
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
--

---
英文摘要：
  An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulae.
---
PDF链接：
https://arxiv.org/pdf/708.0176