Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.     

Canonical forms for quadratic Hamiltonians

Our analysis of the applicable representations of the group of Bogoliubov transformations shows that the diagonalization of a quadratic fermion Hamiltonian with arbitrary complex coefficients is equivalent to the reduction of a skew symmetric matrix to secondary diagonal form by an orthogonal transformation, which we construct explicitly.Similarly, the diagonalization of a positive definite boson Hamiltonian with complex coefficients is equivalent to Whittaker's diagonalization of a symmetric matrix by a symplectic transformatio. Both results are shown to follow from a general spectral theorem for indefinite inner product space, a recent extension of which allows us to block diagonalize a positive definite quadratic boson Hamiltonian with complex coefficients and infinite degrees of freedom and thereby provide a counterpart to Araki's result for Fermi fields.     

Eigenvalue and Eigenfunction of n-Mode Boson Quadratic Hamiltonian

By means of the linear quantum transformation (LQT) theory, a concisediagonalization approach for then-mode boson quadratic Hamiltonian is given,and a general method to calculate the wave function is proposed.     

Quantum Statistics for General Quadratic System

By the generalized linear quantum transformation theory, we concisely derive the analytic expressions of partition function for general quadratic systems of multi-mode boson and fermion Fock space without any information for the energy spectrum. Under a general condition, we firstly acquire the exact expressions of energy spectra for these systems.     

Form factors in the presence of integrable defects

Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors and the transmission factor. The structure of the form factors of defect operators is established in general, and explicitly calculated in particular, for the free boson and for some operator of the Lee–Yang model. Fusion method is also presented to generate boundary form factor solutions for a fused boundary from the known unfused ones.     

基于微观IBM对电子-核散射及核电磁性质的研究(Ⅱ) ME理论方案

从一种微观作用玻色子模型（IBM）玻色子集体态子空间映射出费米子集体态子空间,通过假定玻色子算符形式以及使物理算符在两集体态子空间中对应归一化基矢间矩阵元相等,给出了从费米子单体算符导出玻色子单体算符的一种微观理论方法（ME方法）,文中以获取玻色子结构函数亦即确定玻色子形式核跃迁电荷／电流密度算符为例对此作出了详细介绍,利用微观IBM提供的波函数可在玻色子态空间中求出核跃迁电荷／电流密度,结合电子－核散射以及核电磁跃迁的形式理论,可建立研究电子－核散射各种形状因子与微分散射截面以及核约化跃迁几率,电磁多极矩,核态g因子等物理量的理论方案,在微观sdgIBM-1下利用该方案初步计算了146Nd核21^ 态到o 1^ 态的跃迁电荷密度以及约化跃迁几率,理论结果与实验值符合较好。     

A geometrical representation of the interacting boson model of nuclei

The representation of the interacting boson model hamiltonian as a second-order differential operator in geometrical variables is studied in detail. It is shown that, with appropriate boundary conditions and biorthogonal weight functions, it reproduces exactly both the spectrum and matrix elements of operators of the algebraic boson model. It can be written in self-adjoint form and expanded in a symmetrized moment expansion, allowing the identification of collective mass parameters and energy surfaces, but differs in detail from the conventional geometrical collective model.     

二次型方法求解坐标与动量耦合的n维谐振子能量本征值

借助于数学上的二次型理论,给出一种求解n维坐标与动量耦合的谐振子的普遍方法,并且运用该方法求出了二维和三维坐标与动量耦合的本征值.该方法给出的结论与其他方法相同,说明该方法的正确性,并且由于该方法不需要求出变换矩阵的具体形式,使得运用此方法求解具有对称形式的哈密顿量的本征值问题变得简单,易计算出结果.该方法具有普遍性,...     

n模二次型哈密顿量对角化的一种简单方法

利用线性量子变换理论，对ｎ模Ｂｏｓｅ（Ｆｅｒｍｉ）体系给出了一种简单的对角化方法。     

M1 transitions in the (sdg) boson model

Using the $\text{1}\text{N}$ expansion technique we derive expressions for β→g, γ→g and γ→γ M1 transitions in a general boson model. The M1 matrix elements in the sdg-boson model are similar in form to those in the neutron-proton IBM. Comparisons are made to some selected M1 data exhibiting collective character.     

On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

Newton-Leibniz integration for ket-bra operators (II)—application in deriving density operator and generalized partition function formula

Via the route of applying Newton-Leibniz integration rule to Dirac’s symbolic operators, we show that the density operator e^−βH, where H is multi-mode quadratic interacting boson operators, is a mapping of symplectic transformation in the coherent state representation appearing in the form of non-symmetric ket-bra operator integration. By virtue of the technique of integration within an ordered product (IWOP) of operators, we deduce its normally ordered form which directly leads to the generalized partition function formula and the Wigner function. Some new representations, such as displacement-squeezing correlated squeezed coherent states, constructed by the IWOP technique, also bring convenience in deriving partition functions.     

A schematic model for monopole and quadrupole pairing in nuclei

A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.     

On the Higher Order Effects of A Consistent Q Framework in the sd Interacting Boson Model

By utilizing the 1/N expansion technique(ONET),the analytical expressions of low-lying energy spectrum,the deformation parameter and the reduced matrix elements of E2 transitions to the order of 1/N are systematically given for a consistent Q framework in the sd interacting boson model.It is shown that it is important to consider the angular momentum projection in the intrinsic state formalism.     

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations.     

Dispersion relations for light propagation through a two-level system

Interaction of radiation with two-level system is considered using the Dicke hamiltonian. By making use of the Schwinger representation, the hamiltonian is written in a trilinear form. The hamiltonian is made bilinear by replacing one set of boson operators by C-numbers. A Bogoliubov transformation is then used to reduce the hamiltonian to diagonal form. The density matrix separates into a product of density matrices for separate modes. The energies of the photon-like modes are found to follow dispersion relations which depend on the given set of initial conditions.     

S-Matrix formalism for particles interacting with phonon fields: Coherent state representation

We apply the quasiparticle picture to the interaction between a fermion and a boson field using a coherent states representation of theS matrix. Its matrix elements between single particle states are explicitly evaluated in terms of a path integral. The method is extended to include dispersion in the excitation spectrum and applied to the case of a metal with electron-hole symmetry. Its relation with perturbation theory is discussed and the second order perturbative result for polarons in insulators is recovered.     

Charged Higgs boson production in association with a top quark in MC@NLO

The European Physical Journal C - We discuss the calculation of charged Higgs boson production in association with a top quark in the MC@NLO framework for combining NLO matrix elements with a...     

Various Re-ordering Expressions of General Exponential Quadratic Operators in Mutli-Mode Boson System

In this paper, we give various explicit expressions and transform equalities among usual, normal and anti-normal orderings for the exponential inhomogeneous quadratic (EIQ) operators and their inverse operators in multi-mode boson systems.