The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization...The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △U^2 are less than, equal to, and greater than uncertainties △V^2 for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities,for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.展开更多
In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(...In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(n≥3) cannot be π_1 of any quasi-compact Khlerian manifold.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61475075 and 61170321)
文摘The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △U^2 are less than, equal to, and greater than uncertainties △V^2 for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities,for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.
基金The author is supported partially by NSF of China (19801026, 10171077)
文摘In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(n≥3) cannot be π_1 of any quasi-compact Khlerian manifold.
