Analytic Calculation of Arbitrary Matrix Elements for Boson Exponential Quadratic Operators

By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.     

The boson gas on a Cayley tree

We analyze the free boson gas on a Cayley tree using two alternative methods. The spectrum of the lattice Laplacian on a finite tree is obtained using a direct iterative method for solving the associated characteristic equation and also using a random walk representation for the corresponding fermion lattice gas. The existence of the thermodynamic limit for the pressure of the boson lattice gas is proven and it is shown that the model exhibits boson condensation into the ground state. The random walk representation is also used to derive an expression for the Bethe approximation to the infinite-volume spectrum. This spectrum turns out to be continuous instead of a dense point spectrum, but there is still boson condensation in this approximation.     

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.     

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.     

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。     

多模玻色二次多项式型系统的特性函数和准概率分布函数

运用多模玻色系统广义线性量子变换的普遍理论，对多模玻色二次多项式型系统进行了研究.给出了多模玻色二次多项式型系统的正规、反正规、Wigner特性函数、P表示和Q表示.举例讨论了该系统的压缩性质. 关键词： 多模玻色二次多项式型系统 特性函数 准概率分布函数     

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism. The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept of squeezed boson systems has been applied two-mode bosonic Hamiltonian which is a squeezed one and is determined through a differential equation. This differential equation is solved and energy eigenvalues are found approximately.     

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.     

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.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.     

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.     

二维胶体玻璃中玻色峰与结构无序度的关联

本文从实验上研究了胶体玻璃在相同面密度下随着体系结构无序程度的增加, 振动态密度和玻色峰的变化规律. 通过调制两种不同粒径的温敏性水凝胶的数量比来改变体系的无序程度. 通过分析无序体系的声子模式得到体系的振动特性. 研究发现, 随着无序度的增加, 态密度在低频区域增强、玻色峰增高、玻色峰的峰值向低频区域移动. 不同无序程度的样品引起玻色峰的低频声子模式都表现出准局域的特点, 且低频准局域声子模式与样品中无序结构存在关联.     

Kernel polynomial representation for imaginary-time Green's functions in continuous-time quantum Monte Carlo impurity solver

Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green s functions G(τ),we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver.This representation is based on the kernel polynomial method,which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly.As an illustration of the new representation,we re-examine the imaginary-time Green's functions of the single-band Hubbard model in the framework of dynamical mean-field theory.The calculated results suggest that with carefully chosen integral kernel functions,whether the system is metallic or insulating,the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green's functions have been obtained.     

On electromagnetic properties of rotating nuclei in crpa

An analysis of quasiparticle correlations with special emphasis on transition matrix elements have been done for a self-consistent cranking model. It is pointed out that a second order of the boson representation of a transition operator leads to a signature dependence of transition probabilities between excited one-phonon states in even-even nuclei. Moreover, it brings about the new contribution to an expectation value of electromagnetic moments in the yrast line states of deformed nuclei.     

Multi-photon Rabi model: Generalized parity and its applications

Quantum multi-photon spin–boson model is considered. We solve an operator Riccati equation associated with that model and present a candidate for a generalized parity operator allowing to transform spin–boson Hamiltonian to a block-diagonal form what indicates an existence of the related symmetry of the model.     

Matrix elements of off-diagonal operator equivalents

A simple derivation of off-diagonal operator equivalents and their matrix elements is given in the framework of Schwinger's coupled boson representation of angular momentum theory. The operator equivalents are up to a factor identical with those recently given by Atkins and Seymour, but they are derived differently without making use of properties of spherical harmonics, symmetrization, 3j coefficients and the Wigner-Eckart theorem.     

多项式角动量代数的代数表示及实现

本文利用三参数李群求代数表示的方法求出多项式角动量代数的代数表示及其酉表示，找到一个能同时承载李代数及相对应的多项式角动量代数的基底，并在该基底下求出两种代数之间的联系，利用该联系则也可求出多项式角动量代数的代数表示.最后求出多项式角动量代数的单玻色实现及其在有限维多项式函数空间的微分实现. 关键词： 多项式角动量代数 Higgs代数 su(2)代数     

Self-gravitating bosons at nonzero temperature

A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two phases: the gas and the condensate. By studying the condensation process numerically we determine the critical temperature T_c at which the condensate emerges. As the temperature decreases, the system eventually settles down in the ground state of a cold boson star.     

推导粒子数态波函数的厄米多项式算符法

引入厄米多项式算符并用其正规乘积展开式推导出了粒子数态|n〉在坐标表象和动量表象下的波函数,并由此得出了坐标和动量本征态的福克(Fock)表示形式,这是一个简洁而全新的推导方法.