随机矩阵的本征值外推性质

Property of Extrapolation on Eigenvalues of Random Matrices

外推近似方法在原子核壳模型上取得了一些成功,然而人们对于其原理知道得比较少。这里主要研究并讨论了随机两体系综和高斯正交系综最小本征值。利用截断空间的外推解释了高斯正交系综下的外推公式以及随机两体系综下本征值外推收敛的鲁棒性,即对于壳模型有效相互作用而言,用外推法预言最低本征值收敛性很好。

Although the extrapolation method of diagonalizing the nuclear shell model Hamiltonian is successful, its foundation has not yet been understand very well. In this paper, we study this approach by using random matrices with the focus on gaussian ensemble and two-body random ensemble. We derive the formula of the extrapolation method of diagonalizing the matrices of Gaussian orthogonal ensemble, and discuss the robustness of the extrapolation property by two-body random ensemble. We point out that the extrapolation method of diagonalizing the shell model Hamiltonian works better with the realistic interaction than other interactions.