论文标题
量化Laguerre统一整体结构功能的DIP-RAMP-PLAMP-PLATEAU
Quantifying dip-ramp-plateau for the Laguerre unitary ensemble structure function
论文作者
论文摘要
$ |的合奏平均值\ sum_ {j = 1}^n e^{ikλ_j} |^2 $作为量子混乱的探针，就像其连接的部分一样，是结构函数。为混沌光谱的模型系统绘制这个平均值揭示了所谓的浸入式斜纹形状。将Brézin和Hikami的早期工作推广到高斯单位合奏中，这表明了如何将Laguerre单一合奏的平均值减少到涉及Jacobi单一合奏的光谱密度的表达中。这有助于研究大型$ n $限制，从而量化了浸入式斜坡效应。当laguerre权重$ x^e^e^a e^a e^a e^a e^a e^a e^a e^a e^a e^a e^a e^{ - x} $缩放时，可以找到定量协议的特征特征，以此为高斯单位合奏所知道的特征。但是，对于参数$ a $固定，显示批量缩放的结构函数显示出简单的功能表格$ {2 \foverπ}} {\ rm arctan} \，k $，因此没有Ramp-Plateau Transition。
The ensemble average of $| \sum_{j=1}^N e^{i k λ_j} |^2$ is of interest as a probe of quantum chaos, as is its connected part, the structure function. Plotting this average for model systems of chaotic spectra reveals what has been termed a dip-ramp-plateau shape. Generalising earlier work of Brézin and Hikami for the Gaussian unitary ensemble, it is shown how the average in the case of the Laguerre unitary ensemble can be reduced to an expression involving the spectral density of the Jacobi unitary ensemble. This facilitates studying the large $N$ limit, and so quantifying the dip-ramp-plateau effect. When the parameter $a$ in the Laguerre weight $x^a e^{-x}$ scales with $N$, quantitative agreement is found with the characteristic features of this effect known for the Gaussian unitary ensemble. However, for the parameter $a$ fixed, the bulk scaled structure function is shown to have the simple functional form ${2 \over π} {\rm Arctan} \, k$, and so there is no ramp-plateau transition.
