论文标题
随机基质集合的还原能谱的缩放
Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble
论文作者
论文摘要
我们研究了减少的能源$ \ {e_ {i}^{（n）} \} $，它是通过从Dysen Index Index $β\ eftty的Gaussian Extermement中从每个频谱$ \ {e_ {i} \} $中选择一个级别来构建的。显示为$ \ {e_ {i}^{（n）} \} $具有与$ \ {e_ {e_ {i} \} $相同的概率分布形式，并带有重新缩放的参数$γ= \ frac {n（n+1）} {2} {2}β+n-1 $。值得注意的是，$ \ {e_ {i} \} $以$ \ {e_ {i} \} $为$ \ {e_ {e_ {e_ {i}^{（n）} \} $中的最低级级时，$ n $ th订单级别的间距和非重叠差距比成为$ \ {e_ {e_ {i}^{（n）} \} $的最低级数。数值证据是通过模拟随机自旋链以及对随机矩阵进行建模提供的。我们的结果在超越GOE，GUE，GSE之外的随机矩阵集合中建立了高阶间距分布，并揭示了隐藏在能量谱中的结构的层次结构。
We study the reduced energy spectrum $\{E_{i}^{(n)}\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\{E_{i}\}$, in a Gaussian ensemble of random matrix with Dyson index $β\in \left( 0,\infty \right) $. It's shown $\{E_{i}^{(n)}\}$ bears the same form of probability distribution as $\{E_{i}\}$ with a rescaled parameter $γ=\frac{n(n+1)}{2}β+n-1$. Notably, the $n$-th order level spacing and non-overlapping gap ratio in $\{E_{i}\}$ become the lowest-order ones in $\{E_{i}^{(n)}\}$, hence their distributions will rescale in an identical way. Numerical evidences are provided by simulating random spin chain as well as modelling random matrices. Our results establish the higher-order spacing distributions in random matrix ensembles beyond GOE,GUE,GSE, and reveals a hierarchy of structures hidden in the energy spectrum.
