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原子与分子物理学报

与N 2 分子碰撞产生的Rbγ 2 D态精细结构转移截面的测量

孙献平, 刘子东, 李森林, 刘秩媛, 曾晓云

Published Jan 1, 1990• 0 citations
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On the interpretative aspects of second-order reduced density matrices

Darwin W. Smith, Everett G. Larson, Robert C. Morrison

A division of the 2-matrix Γ, for a system of N identical fermions, into 2 parts is proposed in such a way that Γ has the same 1-matrix γ as does Γ and Γ has a vanishing 1-matrix (and therefore vanishing trace). This is accomplished by evaluating the natural spin orbital (NSO) occupation numbers Γ of Γ from (where the ni are NSO occupation numbers of γ); and letting γ0 have the same NSO's as does γ. The physical interpretation of Γ should be easier with this decomposition, since Γ is completely determined by γ and has a Hartree-Fock-like form, while Γ corrects the pair density of Γ without disturbing its 1-density.

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在~(87)Rb原子中的~(129)Xe核自旋弛豫的研究

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Research of the density-matrix functionals of the periodic Hubbard model

Zheng Yong-lin

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). It is considered that the interaction energy functional w[γij,S] of the Hubbard model is investigated as a function of the single-particle density matrix γij with respect to the lattice sites, and total spin S. Exact numerical results are obtained for w[γij,S] on rings, where γij=γ12 for all nearest neighbors. The properties of w[γij,S] are discussed in the limits of weak (γ012) and strong (γ∞ij) electronic correlations, and in the crossover region γ∞12γ12γ012. Scaling of w[γij,S] in units of the uncorrelated energy w0[γ0ij,S] shows a pseudo-universal behavior as a function of g12=(γ12-γ∞12)/(γ012-γ∞12). In addition, The functional dependence of w[γij,S] is analyzed for different S.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

〈ノート〉多体問題とグリーン関数との関係の研究--グリーン関数と多体問題(24) 量子統計力学(16)

邦夫 橋爪

[synopsis] In this paper, the Bethe-Peierls approximation of the Ising model is interpreted. It is an improvement over the Bragg-Williams approximation of the assumpion N _<++>/2/1γN＝(N_+/N)^2 of a relation between N_<++> and N_+. In the Bethe-Peierls approximation we focus our attention on a sublattice composed of any lattice site plus its γ nearest neighbors. And we find a more accurate relation between N_<++> and N_+. P(S,n) is the probability that n of the nearest neighbors are in a spin-up state while the canter site has the spin state S. From the meaning given to P(S,n) it follows that {(1+L)/2}=N_+/N=Σ^^γ__ P(+1,n) and {(1+σ)/2}=N_<++>/(_γN/2)=(1/γ)Σ^^γ__ nP(+1,n). In our approximation we require that Σ^^γ__ P(+1,n)=(1/γ)x Σ^^γ__ n{P(+1,n)+P(-1,n)}. We assume that P(±1,n)=(1/q)_γC_ne^<1/(k_BT)(±2n±γ)>z^n. z={(1+ze^<2ε/k_BT>)/(z+e^<2ε/k_BT>)}^<γ-1>. L^^-={(z^x-1)/(z^x)+1}, σ^^-[2z^2/{(1+ze)^^<2ε/k_BT>)(1+z^x)}]-1, x≡γ/(γ-1). The internal energy of the Ising lattice in H=0 is U(0,T)=-(1/2)εγ(2σ^^--2L^^-+1). The Curie tempererature T_c is T_c=[(2ε/k_B)/log_e{γ/(γ-2)}] .

•Dec 1, 2012•0 citations

若干Nd^3^＋和Er^3^＋配合物超灵敏跃迁光谱的研究

Menglian Gong, Hua Li

Acta Scientiarum Naturalium Universitatis Sunyatseni•Jan 1, 1994•0 citations
A division of the 2-matrix Γ, for a system of N identical fermions, into 2 parts is proposed in such a way that Γ has the same 1-matrix γ as does Γ and Γ has a vanishing 1-matrix (and therefore vanishing trace). This is accomplished by evaluating the natural spin orbital (NSO) occupation numbers Γ of Γ from (where the ni are NSO occupation numbers of γ); and letting γ0 have the same NSO's as does γ. The physical interpretation of Γ should be easier with this decomposition, since Γ is completely determined by γ and has a Hartree-Fock-like form, while Γ corrects the pair density of Γ without disturbing its 1-density.
The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). It is considered that the interaction energy functional w[γij,S] of the Hubbard model is investigated as a function of the single-particle density matrix γij with respect to the lattice sites, and total spin S. Exact numerical results are obtained for w[γij,S] on rings, where γij=γ12 for all nearest neighbors. The properties of w[γij,S] are discussed in the limits of weak (γ012) and strong (γ∞ij) electronic correlations, and in the crossover region γ∞12γ12γ012. Scaling of w[γij,S] in units of the uncorrelated energy w0[γ0ij,S] shows a pseudo-universal behavior as a function of g12=(γ12-γ∞12)/(γ012-γ∞12). In addition, The functional dependence of w[γij,S] is analyzed for different S.
[synopsis] In this paper, the Bethe-Peierls approximation of the Ising model is interpreted. It is an improvement over the Bragg-Williams approximation of the assumpion N _<++>/2/1γN＝(N_+/N)^2 of a relation between N_<++> and N_+. In the Bethe-Peierls approximation we focus our attention on a sublattice composed of any lattice site plus its γ nearest neighbors. And we find a more accurate relation between N_<++> and N_+. P(S,n) is the probability that n of the nearest neighbors are in a spin-up state while the canter site has the spin state S. From the meaning given to P(S,n) it follows that {(1+L)/2}=N_+/N=Σ^^γ__ P(+1,n) and {(1+σ)/2}=N_<++>/(_γN/2)=(1/γ)Σ^^γ__ nP(+1,n). In our approximation we require that Σ^^γ__ P(+1,n)=(1/γ)x Σ^^γ__ n{P(+1,n)+P(-1,n)}. We assume that P(±1,n)=(1/q)_γC_ne^<1/(k_BT)(±2n±γ)>z^n. z={(1+ze^<2ε/k_BT>)/(z+e^<2ε/k_BT>)}^<γ-1>. L^^-={(z^x-1)/(z^x)+1}, σ^^-[2z^2/{(1+ze)^^<2ε/k_BT>)(1+z^x)}]-1, x≡γ/(γ-1). The internal energy of the Ising lattice in H=0 is U(0,T)=-(1/2)εγ(2σ^^--2L^^-+1). The Curie tempererature T_c is T_c=[(2ε/k_B)/log_e{γ/(γ-2)}] .