论文标题
双变量$ q $ - 正常分布的过渡强度分布分布从$ k $ - 体互动生成的许多粒子随机矩阵合奏
Bivariate $q$-normal distribution for transition strengths distribution from many-particle random matrix ensembles generated by $k$-body interactions
论文作者
论文摘要
最近，通过较低的矩确定，单变量Q-正常分布（这是$ q $ hermite多项式的重量函数）描述了由$ k $ k $ - body Itspactress产生的许多晶状体随机矩阵ENSRIX的合奏平均特征值密度[Manan Vyas and V.K.B.B. Kota，J。Stat。机械。 {\ bf 2019}，103103（2019）]。这些合奏通常称为$ k $ body互动[ee（$ k $）]的嵌入式合奏，他们的goe和gue版本分别称为egoe（$ k $）和egue（$ k $）。 Going beyond this work, the lower order bivariate reduced moments of the transition strength densities, generated by EGOE($k$) [or EGUE($k$)] for the Hamiltonian and an independent EGOE($t$) for the transition operator ${\cal O}$ that is $t$-body, are used to establish that the ensemble averaged bivariate transition densities follow the bivariate $ Q $ - 正态分布。呈现的也是双变量相关系数$ρ$的公式和$ q $值作为粒子数量$ m $的函数，单个粒子的数量，粒子占据的单个粒子状态$ n $分别排名$ k $和$ t $ $ h $ $ h $和$ h $和$ h $和$ {\ cal o} $。最后，提出了使用Bivariate $ Q $ QUANTOR表格A的公式，用于从具有能源$ E $的州的过渡强度中的混乱量度量度量度量度。
Recently it is established, via lower order moments, that the univariate q-normal distribution, which is the weight function for $q$-Hermite polynomials, describes the ensemble averaged eigenvalue density from many-particle random matrix ensembles generated by $k$-body interactions [Manan Vyas and V.K.B. Kota, J. Stat. Mech. {\bf 2019}, 103103 (2019)]. These ensembles are generically called embedded ensembles of $k$-body interactions [EE($k$)] and their GOE and GUE versions are called EGOE($k$) and EGUE($k$) respectively. Going beyond this work, the lower order bivariate reduced moments of the transition strength densities, generated by EGOE($k$) [or EGUE($k$)] for the Hamiltonian and an independent EGOE($t$) for the transition operator ${\cal O}$ that is $t$-body, are used to establish that the ensemble averaged bivariate transition densities follow the bivariate $q$-normal distribution. Presented are also formulas for the bivariate correlation coefficient $ρ$ and the $q$ values as a function of the particle number $m$, number of single particle states $N$ that the particles are occupying and the body ranks $k$ and $t$ of $H$ and ${\cal O}$ respectively. Finally, using the bivariate $q$ normal form a formula for the chaos measure number of principal components (NPC) in the transition strengths from a state with energy $E$ is presented.
