单模系综的谱统计
Spectral statistics of the uni-modular ensemble
摘要：
本文研究了在大矩阵规模的限制下，从U（1）中均匀选取元素的厄米矩阵的谱统计特性，即单模系综（UME）.使用三种互补方法;超对称积分方法、组合图论分析和布朗运动方法，我们能够导出平均谱矩的1/N修正的表达式，并分析了关于这个平均值的波动。通过从三个不同的角度处理同一个系综，我们可以批判性地比较它们的相对优势，并得到一些新的结果。
英文摘要：
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able to derive expressions for 1/N corrections to the mean spectral moments and also analyse the fluctuations about this mean. By addressing the same ensemble from three different point of view, we can critically compare their relative advantages and derive some new results.
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