双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符,利用有序算符内的积分（IWOP）技术分析了其变换特性,并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

纠缠态投影算符的积分

借助湮没算符的本征值方程及其本征态的完备性,证明了纠缠态的完备性．在此基础上,利用纠缠态所满足的本征值方程,得到了非对称纠缠态投影算符的积分． 关键词： 完备性 纠缠态 投影算符 积分     

坐标算符本征矢的表示与不对称投影算符的积分

借助于粒子数算符的本征态和坐标算符函数的本征方程,把坐标算符的本征矢〈f(x)|表示为一个算符对坐标本征矢〈x|的作用.由此,把不对称的坐标投影算符转换为对称的坐标投影算符,再利用坐标本征矢的完备性,给出不对称坐标投影算符的积分. 关键词： 本征矢 算符的积分 本征方程 完备性     

坐标本征矢的谐振子表示及完备性

借助粒子数算符的本征矢及其完备性,得到了用实数x、产生算符及粒子基态表示的矢量|x〉.以此为起点,证明了矢量|x〉是坐标算符的本征矢,坐标投影算符的积分是单位算符,坐标本征矢是正交归一的.因此,坐标本征矢集{|x〉}具有正交归一性和完备性.     

基于坐标表象的脊波变换研究

在小波变换量子力学机制的启发下, 通过采用Fock空间里双模坐标本征态改写经典Ridgelet变换, 定义了量子光学态的Ridgelet变换. 然后利用IWOP技术给出不对称积分算符的显式, 并推导出了两个有用的双模算符正规乘积公式. 在此基础上, 通过选取双模“墨西哥帽”母小波函数, 分析了相干态、特殊压缩相干态、中介纠缠态表象的Ridgelet变换. 关键词： IWOP技术 Ridgelet变换 相干态     

论双模压缩算符的自然表象——纠缠态表象

利用简洁的幺正变换得到双模压缩算符在纠缠态中表示,使用同样的方法可得到双模压缩算符在坐标和动量本征态中的表示。     

广义n维耦合谐振子体系的代数解法

利用二次型理论,通过三次保对易线性变换,实现了广义n维耦合谐振子体系哈密顿量的退耦合, 得到了体系对角化后的哈密顿量,并给出了体系的能量本征值和本征函数.     

介观互感耦合阻尼并联双谐振电路的量子涨落

对介观互感耦合阻尼并联电路作双模耦合阻尼谐振子处理,将其量子化.通过三次幺正变换,将体系的哈密顿量对角化.在此基础上给出了体系的本征能谱,研究了Fock态、真空态下各回路电流和电压的量子涨落.     

关于多电子体系的投影算符的注记

按照群论方法对多电子体系的对称化投影算符进行了讨论，并用投影算符和升降算符推出多电子的自旋态。     

求坐标表象中压缩算符显式的3种方法

分别用提取变量积分法、正规乘积内的积分技术及投影算符转换法,得到了坐标表象中压缩算符的显式.     

自旋为任意整数的传播子

以自旋为任意整数的自由粒子的波函数(Bargmann-Wigner方程的解)为基础，进一步研究了 自旋为任意整数的投影算符和传播子.证明了Behrends和Fronsdal所构造的投影算符是正确 的.导出了自旋为任意整数的场的一般对易规则和费恩曼传播子的一般表达式. 关键词： 整数自旋 投影算符 对易规则 费恩曼传播子     

A mixed integral equation of mechanics and a generalized projection method of its solution

A mixed multidimensional integral equation containing integral operators of various types is studied. The case in which the equation has one compact, self-adjoint, and strongly positive operator (with constant limits of integration) and two non-self-adjoint integral Volterra operators (with a variable upper limit of integration) is considered. To solve the equation, an effective projection method allowing one to obtain the result in a form with explicitly distinguished principal singularities is proposed.     

Linked-cluster expansions in the equations of motion method for nonequilibrium processes

For an arbitrary irreversible process taking place in a closed physical system equations of motion are derived directly from the Liouville equation without introducing any projection operator. These equations are of nonmarkowian nature and are exactly valid for any system arbitrarily far from equilibrium. Using field-theoretical techniques the integral kernels in these equations are expanded into a diagram perturbation series which is proved to be linked. For a system having short memory it is shown that the secular divergent terms cancel each other. Then, using the diagram language the equations of motion are obtained in a much simpler form.     

Optimally chosen Nakajima–Zwanzig master equation for mean field approximation

We define an ensemble of projection operators, each of which has an exact associated Nakajima–Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields a completely determined inhomogeneous master equation for every projection operator. A specific projection operator is then chosen so that the master equation optimally matches an abstract mathematical form which preserves positivity, complete positivity, and correctly equilibrates. We study a nitrogen vacancy center in diamond interacting with ¹³C impurities to illustrate the method.     

On the calculation of memory functions for nonlinear irreversible processes

A linear inhomogeneous Volterra integral equation for the memory functions of the nonlinear theory of irreversible processes is derived. No projection operator is involved. Recursion relations for the solution of the integral equation are given. If the kernels are expanded about equilibrium, the exact linear and nonlinear Onsager coefficients are obtained.     

The group with Grassmann structureUOSP(1.2)

The finite-dimensional representations of the Lie superalgebraosp(1.2) and the group with Grassmann structureOSP(1.2) have been studied. The explicit expression of the projection operator of the superalgebraosp(1.2) has been found. The operator permits an arbitrary finite-dimensional representation to be expanded in the components multiple to the irreducible ones. The Clebsch-Gordan coefficients for the tensor product of two arbitrary irreducible representations have been obtained. The matrix elements of the irreducible representations of the groupUOSP(1.2) [the analoque of the compact form of the groupOSP(1.2)] are studied. The explicit form of these matrix elements, the differential equations satisfied by them, and the integral of their product have been found.     

Projection operators in nuclear structure calculations

Projection operators are an important tool in nuclear structure theory, because in many circumstances it is useful to construct wave-functions ψ which are not eigenfunctions of some operator Λ, although it is apparent that the physical states must be eigenstates of that operator. Thus one first constructs ψ and then projects from it onto eigenfunctions of Λ. We discuss the cases of angular momentum, isospin, centre of mass energy, particle number and antisymmetry. We describe the integral projection operator, an expansion in shift operators, the product operator of Löwdin and another product operator (the cosine product). Certain methods which appear in the literature are seen to be equivalent to one or the other of these. We consider factors that influence the choice of an appropriate method. Projection occurs frequently in the context of a variational method (such as Hartree-Fock or BCS). We consider the question of projection before or after variation.     

Semi-group approach to multiperipheral dynamics

We consider the multiperipheral integral equation at vanishing four-momentum transfer in the form given by Chew and de Tar and we remark that the angular integrations can be interpreted as a convolution of measures defined in a semi-group S contained in the Lorentz group. We study the geometrical properties and a class Banach-space representations of this semi-group. By projection on these representations, we perform a partial wave analysis of the multiperipheral equation. Under some physically very natural conditions, we prove that the projection integrals converge, the partial wave amplitudes are analytic in a half-plane of the complex angular momentum and the kernel of the partial wave equation represents a bounded operator. We give a preliminary discussion of the inversion problem, i.e., of the construction of the amplitude from its partial wave projections.