随机Hamilton算子的最低特征值
Lowest Eigenvalues of Random Hamiltonians
摘要：
本文给出了费米子和玻色子系统随机哈密顿量的最低本征值。我们证明了一个用能量重心和本征值宽度计算随机哈密顿量最低本征值的经验公式，它适用于许多不同的系统（除了$d$玻色子系统）.我们通过增加大于2的矩来提高公式的精度。本文提出了另一个计算大维数随机矩阵（20-5000）最低特征值的新公式。这些经验公式不仅适用于计算最低能量，而且也适用于计算无规两体相互作用下系统的激发能。
英文摘要：
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
