随机矩阵理论的非广延和超统计推广
Nonextensive and superstatistical generalizations of random-matrix theory
摘要：
随机矩阵理论（RMT）基于两个假设：（1）矩阵元素独立性，（2）基不变性。大多数提出的推广保留了第一个假设，违反了第二个。最近，几位作者提出了其他版本的理论，保持基础上允许矩阵元素之间的相关性为代价的不变性。这是通过从非广延熵而不是标准的香农熵开始，或者遵循最近提出的超统计概念的基本规定来实现的。我们回顾了RMT的这些推广，并通过计算最近邻间距分布，并将计算结果与实验结果和从有序到混沌过渡的系统的数值实验结果进行比较来说明它们的价值。
英文摘要：
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep base invariance on the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or following the basic prescription of the recently suggested concept of superstatistics. We review these generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments and numerical-experiments on systems in transition from order to chaos.
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