随机逆循环矩阵与屏蔽谐振子
Random reverse-cyclic matrices and screened harmonic oscillator
摘要：
我们计算了随机逆循环矩阵的联合概率分布函数，并证明了它与一个N体精确可解模型有关。我们把这个著名的模型势称为屏蔽谐振子。这种联系使我们能够得到在屏蔽谐振势中运动的粒子位置之间的所有关联。这个合奏的非平凡特征值的密度被发现是维格纳形式，并承认在原点的孔，在相反的高斯正交合奏的随机矩阵的循环法。间距分布呈现不同的形式，从高斯型到维格纳型。
英文摘要：
We have calculated the joint probability distribution function for random reverse-cyclic matrices and shown that it is related to an N-body exactly solvable model. We refer to this well-known model potential as a screened harmonic oscillator. The connection enables us to obtain all the correlations among the particle positions moving in a screened harmonic potential. The density of nontrivial eigenvalues of this ensemble is found to be of the Wigner form and admits a hole at the origin, in contrast to the semicircle law of the Gaussian orthogonal ensemble of random matrices. The spacing distributions assume different forms ranging from Gaussian-like to Wigner.
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