Method for construction of operators in Fock space

It is shown, by providing a general method for the construction that any Fock space linear operator defined on the dense linear manifold spanned by the particle number representation basis can be represented in terms of the annihilation and creation operators. The normal form of the representation is unique.     

截断误差导致的非双曲不动点邻域拓扑变异

提供一个关于截断误差使简单系统复杂化的直接实验证据,以此证明存在混沌抗退化机理.分别构造了一个一维圆弧迭代系统和一个一维抛物线迭代系统,两者均有一个非双曲不动点,其迭代序列被证明是简单极限序列,数字计算实验显示这两个迭代系统都存在可以越过不动点的序列.采用计算"元胞"分析方法清晰地展示了截断误差导致非双曲不动点邻域拓扑变异:形成第I类阵发混沌通道,或产生纹波分岔.     

Shell model spectra of92Tc and93Ru

Shell model calculations for the nuclei⁹¹Mo,⁹²Tc and⁹³Ru in the Talmi approach have been done. The ground state binding energies and the excitation spectra agree with experiment.     

Effective interaction in non-degenerate model space

The effective interaction in a model space has been calculated by the Krenciglowa–Kuo (KK) and the Lee–Suzuki (LS) iterative methods, both of which assume that the unperturbed energies in the model space are degenerate. We generalize these two methods in a natural and simple manner so that they apply also to non-degenerate model spaces. The key to the generalization is to use the effective hamiltonian instead of the effective interaction in the formulation of iterative schemes. Using test calculations in a simple model, we demonstrate that the new methods work excellently.     

Recursive calculation of matrix elements for the generalized seniority shell model

A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of one-body and two-body operators and basis state overlaps.     

同步三通道激光告警光学系统有效孔径的确定及截获能量的估算

为了确定一种同步三通道激光告警光学系统的有效孔径并估算截获能量,建立了激光辐照远场传输模型,仿真研究了远场光斑半径、单通道入瞳半径和通道间相对能量差之间的数值关系.仿真结果表明:各通道之间最大相对能量差与远场光斑中心能量密度的大小无关,在激光远场光斑边沿处各通道之间的相对能量差最大;最大相对能量差限定时,远场光斑半径越大,允许的单通道入瞳半径也越大,但相应系统截获的脉冲能量或脉冲功率却相对减小;最大能量差限定为1%,远场光斑半径分别为2.5 m,4.0 m和7.5 m时,允许的最大单通道入瞳半径分别为3 mm, 5 mm和10 mm,相应系统截获的最大脉冲能量为1.14×10-5 J,7.54×10-6 J和2.68×10-6 J,最大脉冲功率为1.63 W, 1.08 W和0.38 W.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Frontiers and challenges of the nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 1 May 2001 / Accepted: 4 December 2001     

Density and fluctuations in shell model spectra

A simple method, based on the Gram-Charlier expansion, to separate the smooth and fluctuating parts of the level density is developed. Applications to spectra arising from large shell model calculations are considered. Fluctuations in the energy levels are studied. It is found that with this proper decomposition, even long range correlations agree with the predictions of the random matrix theory.     

The nucleon pair approximation(NPA) of the shell model

In this paper we discuss the nucleon pair approximation of the shell model,based on our recent results which include a brief introduction to its framework and validity.We exemplify this model by studies of low-lying states for odd-odd nuclei in the mass number A-210 region.     

Frontiers and challenges of nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: otsuka@phys.s.u-tokyo.ac.jp     

Discrete phase space I. Finite difference operators and lattice Schrödinger wave equation

A new representation of quantum mechanics involving finite difference operators is presented. The time-dependent Schrödinger wave equation is furnished as a partialdifference-differential equation. This wave equation is solved exactly for a three-dimensional oscillator.It is emphasized that this representation is exact and not a numerical approximation.     

Exact and model operators for magnon-phonon interactions in antiferromagnets

A theoretical study is given of magnon-phonon interactions in antiferromagnetic materials. The roles of magnons and phonons as heat carriers and as sources of thermal resistance have been taken into consideration. The exact collision operator which represents the magnon-phonon interactions involved in the transport Boltzmann equations has been replaced by a model operator which possesses the same important properties. The effect of other scattering processes that either phonons or magnons are involved has also been investigated. A new expression for the thermal conductivity has been derived. It includes terms which represent both Normal and Umklapp magnon-phonon processes. The results obtained by using the new expression agree quantitatively with the experimental measurements on Fe Cl₂     

Effective quadrupole operators for the second half of the 2p-1f shell

The one body matrix elements of the effective quadrupole operator in the 2p _3/2, 1f _5/2 2p _1/2 configurations have been calculated taking into account the renormalization effects due to excitations from the closed 1f _7/2 shell. First and second order perturbations of the residual interaction as well as an infinite series involving one particle-one hole core excitations are considered. The results are used to calculate quadrupole moments of odd mass nuclei together withBE 2 values between low-lying states. Agreements with experimental results, whereever known, are seen to be generally greatly improved.     

Invariant subspaces of clustering operators

A class of clustering operators is defined which is a generalization of a transfer matrix of a Gibbs lattice field with an exponential decay of correlations. It is proved that for small values of the clustering operator has invariant subspaces which are similar tok-particle subspaces of the Fock space. The restriction of the clustering operator onto these subspaces resembles the operator exp(-H _k, whereH _k is thek- particle Schrödinger Hamiltonian in nonrelativistic quantum mechanics. The spectrum of eachH _k,k1, is contained in the interval (C ₁^k,C ₂^k). These intervals do not intersect with each other.     

Structure of unstable nuclei in the sd-pf shell region by shell model with proper tensor force

Focusing on the importance of the tensor force in the effective interaction, we investigate the structure of unstable nuclei around N=28 with large-scale shell-model calculations. From the analysis of the spin-tensor decomposition for some interactions, the tensor force in the effective interaction should be close to the π+ ρ force, whereas it is much weaker in the Millener-Kurath (MK) interaction which is often used as the cross-shell interaction. The significance of the tensor force appears in the structure around ⁴²Si: the proper tensor force predicts that it is deformed contrary to the result from MK.     

A shell model for the H-bonded ferroelectric KH2PO4

A shell model for KH₂PO₄ (KDP), the prototype compound of the family of H-bonded ferroelectric materials, has been constructed by adjusting the interaction parameters to first-principles calculations. Structural properties, energy barriers, phonons, and the relative stability between the ferroelectric (FE) phase and a relevant antiferroelectric metastable structure associated to domain walls, compare very favorably to available first-principles and experimental data. Molecular dynamics simulations show that the model behaves satisfactorily within the FE phase. This model will be used to study the elusive structure of the paraelectric (PE) phase and the nature of the FE–PE phase transition.     

再谈相干态在算符编序中的应用

利用广义Weyl对应导出了相干态密度算符的S-编序表示.通过此表示并结合S-编序内的算符积分技术,导出了若干量子玻色算符的S-编序形式(包含了正规编序、Weyl编序和反正规编序).此方法进一步推广了相干态在算符编序中的应用.     

Effective potential in curved space and cut-off regularizations

We consider derivation of the effective potential for a scalar field in curved space-time within the physical regularization scheme, using two sorts of covariant cut-off regularizations. The first one is based on the local momentum representation and Riemann normal coordinates and the second is operatorial regularization, based on the Fock-Schwinger-DeWitt proper-time representation. We show, on the example of a self-interacting scalar field, that these two methods produce equal results for divergences, but the first one gives more detailed information about the finite part. Furthermore, we calculate the contribution from a massive fermion loop and discuss renormalization group equations and their interpretation for the multi-mass theories.     

Study of the microstructure and mechanical properties of white clam shell

The microstructure and mechanical properties of white clam shell were investigated, respectively. It can be divided into horny layer, prismatic layer and nacreous layer. Crossed-lamellar structure was the microstructural characteristic. The extension direction of lamellae in prismatic layer was different from that in nacreous layer, which formed an angle on the interface between prismatic layer and nacreous layer. The phase component of three layers was CaCO₃ with crystallization morphology of aragonite, which confirmed the crossed-lamellar structural characteristic. White calm shell exhibited perfect mechanical properties. The microhardness values of three layers were 273 HV, 240 HV and 300 HV, respectively. The average values of flexure and compression strength were 110.2 MPa and 80.1 MPa, respectively. The macroscopical cracks crossed the lamellae and finally terminated within the length range of about 80 μm. It was the microstructure characteristics, the angle on the interface between prismatic and nacreous layer and the hardness diversity among the different layers that enhanced mechanical properties of white calm shell.