We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. Th...We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. The corre-sponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are given.展开更多
In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalize...In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalizedpseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to berelevant to polynomial angular momentum algebras.展开更多
The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invar...The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.展开更多
Using both the fermionic-kike and the bosonic-like properties of the Paulispin operators σ_+, σ_-, and σ_z we discuss the derivation of Bose description of the Pauli spinoperators originally proposed by Shigefumi N...Using both the fermionic-kike and the bosonic-like properties of the Paulispin operators σ_+, σ_-, and σ_z we discuss the derivation of Bose description of the Pauli spinoperators originally proposed by Shigefumi Naka, and deduce another new bosonic representation ofPauli operators. The related coherent states, which are nonlinear coherent state and coherent spinstates for two spins, respectively, are constructed.展开更多
In the preceding paper （Commun. Theor. Phys. 51 （2009） 321） we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators ...In the preceding paper （Commun. Theor. Phys. 51 （2009） 321） we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly desentangle the form of exp[2hJz ＋ g J＋ ＋ kJ_] as the ordering exp（... J＋）exp（... Jz）exp（... J_）, we employ the Schwinger Bose realization J_ = bta, J＋ = atb, Jz=（ata - btb）/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator＇s desentanglng is different from its decomposition in normal ordering.展开更多
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
文摘We obtained for the Higgs algebra three kinds of single boson realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization, and the unitary Villain-like realization. The corre-sponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are given.
文摘In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalizedpseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to berelevant to polynomial angular momentum algebras.
文摘The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.
文摘Using both the fermionic-kike and the bosonic-like properties of the Paulispin operators σ_+, σ_-, and σ_z we discuss the derivation of Bose description of the Pauli spinoperators originally proposed by Shigefumi Naka, and deduce another new bosonic representation ofPauli operators. The related coherent states, which are nonlinear coherent state and coherent spinstates for two spins, respectively, are constructed.
基金Supported by the Natural Science Foundation of Heze University of Shandong Province,China under Grant No.XY07WL01the University Experimental Technology Foundation of Shandong Province under Grant No.S04W138
文摘In the preceding paper （Commun. Theor. Phys. 51 （2009） 321） we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly desentangle the form of exp[2hJz ＋ g J＋ ＋ kJ_] as the ordering exp（... J＋）exp（... Jz）exp（... J_）, we employ the Schwinger Bose realization J_ = bta, J＋ = atb, Jz=（ata - btb）/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator＇s desentanglng is different from its decomposition in normal ordering.
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.
