论文标题
圆形统一合奏的功率谱
Power spectrum of the circular unitary ensemble
论文作者
论文摘要
我们研究了从圆形统一集合$ {\ rm cue}（n）$中绘制的随机矩阵的特征角度的功率谱，并表明可以根据弗雷姆尔姆的决定因素或toeplitz的确定性或第六个pachlevé函数对其进行评估。 In the limit of infinite-dimensional matrices, $N\rightarrow\infty$, we derive a ${\it\, concise\,}$ parameter-free formula for the power spectrum which involves a fifth Painlevé transcendent and interpret it in terms of the ${\rm Sine}_2$ determinantal random point field.此外，我们讨论了预测的功率谱法的普遍性并将其制成表格（遵循http://eugenekanzieper.faculty.hit.ac.al/data.html），以便于随机-matrix-theory和量子混沌练习者。
We study the power spectrum of eigen-angles of random matrices drawn from the circular unitary ensemble ${\rm CUE}(N)$ and show that it can be evaluated in terms of either a Fredholm determinant, or a Toeplitz determinant, or a sixth Painlevé function. In the limit of infinite-dimensional matrices, $N\rightarrow\infty$, we derive a ${\it\, concise\,}$ parameter-free formula for the power spectrum which involves a fifth Painlevé transcendent and interpret it in terms of the ${\rm Sine}_2$ determinantal random point field. Further, we discuss a universality of the predicted power spectrum law and tabulate it (follow http://eugenekanzieper.faculty.hit.ac.il/data.html) for easy use by random-matrix-theory and quantum chaos practitioners.
