The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar p...The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.展开更多
It has been widely accepted that spherical per- iodicity generally dominates liquid and amorphous structure formation, where atoms tend to gather near spherically peri- odic shells according to Friedel oscillation. He...It has been widely accepted that spherical per- iodicity generally dominates liquid and amorphous structure formation, where atoms tend to gather near spherically peri- odic shells according to Friedel oscillation. Here it is revealed that the same order is just hidden in the atomic global packing modes of the crystalline phases relevant to bulk metallic glasses. Among the multiple nearest-neighbor dusters devel- oped from all the non-equivalent atomic sites in a given phase, there always exists a principal duster, centered by which the spherical periodicity, both topologically and chemically, is the most distinct. Then the principal dusters plus specific glue atoms just constitute the cluster-plus-glue-atom structural units shared by both metallic glasses and the corresponding crystalline phases. It is further pointed out that the spherical periodicity order represents the common structural homology of crystalline and amorphous states in the medium-range through scrutinizing all binary bulk-glass-relevant phases in Cu-（Zr, Hf）, Ni-（Nb, Ta）, Al-Ca, and Pd-Si systems.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11105097,10975075,and 11175089the National Basic Research Program of China under Grant No.2012CB921900the National Research Foundation and Ministry of Education,Singapore under Grant No.WBS:R-710-000-008-271
文摘The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.
基金supported by the Science Challenge Program (JCKY2016212A504)the National Natural Science Foundation of China(11674045)
文摘It has been widely accepted that spherical per- iodicity generally dominates liquid and amorphous structure formation, where atoms tend to gather near spherically peri- odic shells according to Friedel oscillation. Here it is revealed that the same order is just hidden in the atomic global packing modes of the crystalline phases relevant to bulk metallic glasses. Among the multiple nearest-neighbor dusters devel- oped from all the non-equivalent atomic sites in a given phase, there always exists a principal duster, centered by which the spherical periodicity, both topologically and chemically, is the most distinct. Then the principal dusters plus specific glue atoms just constitute the cluster-plus-glue-atom structural units shared by both metallic glasses and the corresponding crystalline phases. It is further pointed out that the spherical periodicity order represents the common structural homology of crystalline and amorphous states in the medium-range through scrutinizing all binary bulk-glass-relevant phases in Cu-（Zr, Hf）, Ni-（Nb, Ta）, Al-Ca, and Pd-Si systems.
