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利用推广的BCS平均场理论,考虑随机矩阵理论所给予的能级统计和关联,推导得出了适合奇偶两种电子数宇称的统一公式,将公式用到3个Gauss系综的计算结果表明,对于总自旋为零的Gauss正交系综(GOE)和Gauss幺正系综(GUE)中的金属小粒子,可以从理论上再现金属小粒子随其尺寸变小,所出现的超导电性先增强后衰减到零连续变化的实验现象,而对Gauss辛系综(GSE)中的金属小粒子,只有超导电性逐步衰减到零的现象.经分析发现,金属小粒子的超导增强现象来自于电子配对、轨道自旋耦合强度与外磁场强度的平衡,而后者只有在计算中考虑系综的能谱统计特征才能体现.
Based on the extended BCS average field theory and the energy level statistics and correlations given by stochastic matrix theory, a unified formula suitable for both parity of odd and even numbers is deduced. Using the results of three Gauss ensembles, , For small metal particles in Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary Ensemble (GUE) with zero total spin, the small metal particles can be reproduced in theory as their size decreases. The superconductivity However, for the small metal particles in Gauss symplectic ensemble (GSE), only the superconductivity gradually decays to zero. The analysis shows that the superconducting enhancement of small metal particles Phenomenon comes from the electronic matching, orbital spin coupling strength and the balance of the external magnetic field strength, while the latter only in the calculation of ensemble energy spectrum statistics can be reflected.