The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.
ZHENG Renrong1 CHEN Zhiqian2 & ZHU Shunquan1,3 1. Department of Physics, Shanghai Normal University, Shanghai 200234, China
For a two-particle (spin 1/2) system, three fundamental forms of complete sets of commuting observables (CSCO) composed of two-body operators s 1as 2b are given. The corresponding simultaneous eigenstates constitute three types of maximally entangled states, one of which is the well known Bell basis. This paper discusses the possible pairs of spin observables whose simultaneous measurement outcomes are definitely correlated in probabilistic fashion.
RUAN Manqi, XU Gang & ZENG Jinyan Department of Physics, Tsinghua University, Beijing 100084, China
