李超代数OSP（1,2）的两分量相干态表示

本文构造了李超代数ＯＳＰ（１，２）的一种新的相干态－－两分量相干态。这种两分量相干态形成ＯＳＰ（１，２）代数的一种新表示。获得了ＯＳＰ（１，２）代数的一种非齐次微分实现。分析了这种新相干态的压缩性质。发现ＯＳＰ（１，２）代数的奇生成元可以改变这种两分量相干态的压缩性质。     

量子代数SUq（4）的多分量q相干态表示

引入SUq（4）的多分量q相干态，讨论了密度算符在这种相干态中的表示和生成元的非齐次微分实现．     

非谐振子Gazeau-Klauder与Klauder-Perelomov相干态

利用Kinani-Daoud方法构造了非谐振子势的Gazeau-Klauder(GK)相干态和Klauder-Perelomov(KP)相干态，表明两种相干态在非线性谐振子势下具有完全不同的形式，并对两种相干态的完备性以及各自构成的Hilbert空间进行了讨论. 对相干态的Mandel Q参数的研究表明：GK相干态服从亚Poisson统计分布，KP相干态服从超Poisson统计分布.     

psl（2｜2）^（2）k非线性σ-模型超对称性质研究

由psl（2｜2）^（2）k非线性σ-模型加上WZ-项得到的WZW模型足共形场论,它具有李超代数psl（2｜2）对称性.该文用向量相干态方法给出了李超代数psl（2｜2）的微分算子表示.并在此基础上给出了扭曲Kac-Moody李超代数psl（2｜2）^（2）k自由场实现,相应共形场论的中心荷为-2.     

3-空间曲面上的一个重要向量场及相关结果

设 ｆ：Ｍ２（Ｃ）→ Ｎ３（ｃ）是 ２－维黎曼流形 Ｍ２到 ３维空间形式 Ｎ３（Ｃ）的等距浸入．找到一个由Ｍ２的第二基本形式确定的向量场 δ ，使得高斯曲率 Ｋ表为其散度 Ｋ＝ ｄｉｖ（δ）．在 Ｎ３（ｃ）＝ Ｅ３的情形，证明了ｆ可保持反定向高斯映射共形形变的充要条件是δ为闭向量场．对于可保持反定向高斯映射共形形变的曲面，本文给出了其形变象的表示公式     

一类量子态的迹距离相干度量的最优化证明方法

迹距离相干度量是基于迹范数提出的量化相干的一种度量.然而,很难给出一般量子态迹距离相干度量的表达式并且找到对应的最近非相干态.通过最优化方法给出了一类d×d量子态的迹距离相干度量,并且证明了这类量子态的最近非相干态就是由该量子态去掉所有非对角元素得到的对角矩阵.     

关于相干态的若干新应用

本文把量子场论中算符的正规乘积应用于相干态。利用正规乘积下的积分方法可以简捷地导出一系列新的量子算符公式、某些著名的么正变换和泛函积分的转换矩阵元、给出了Wigner算符的显示形式和相干态形式,并由此分别就玻色、费米两种情况证明了Weyl对应的实质是相干态对应,其中费米子Weyl对应和Wigner算符是根据费米子相干态的理论给出的,由它可以进一步导出无边界项的费米子泛函积分、母泛函、费米子Wigner定理和Moyal括号,从而建立了费米系统量子力学及其赝经典对应的理论。     

关于同伦满态与覆叠空间

本文在点标道路连通ＣＷ空间的同伦范畴中，利用同伦推出示性了同伦满态，得出了若ｆ：Ｘ－Ｙ是同伦满态，则对π１Ｙ的任一正规子群Ｈ，升腾映射ｆ：Ｘ（ｆ－１＃（Ｈ））→■（Ｈ）也是同伦满态．     

一类复杂Feynman转换矩阵元的计算

本文利用相干态的性质把相互作用表象中演化算符所满足的方程化为相干态对应c数方程,并用正规乘积内积分法求出了平方型含时外源和线性含时外源共存时的谐振子Feynman转换矩阵元的一般形式。     

量子孤子的噪声极限及准相干态

基于量子非线性SchrÖdinger方程的严格解和量子孤子态的定义,分析了光孤子的量子噪声,得出其局域粒子数和正交位相分量的噪声的最低极限,证明其不可能低于相干态下相应值,即对基孤子态该力学量的起伏不可能被压缩.还进一步表明,局域粒子数和正交位相分量取最低噪声的态均为准孤子相干态,在该态下量子孤子的波包扩散和相位扩散效应可以忽略.     

Analytic Representations Based on SU(1,1) Lie Algebra Coherent States for Squeezed Displaced Fock States

The coherent states (CSs) of the SU(1,1) group can be divided into two broad categories: (a) the Barut-Girardello coherent states (BGCSs) and (b) the Perelomov coherent states (PCSs). Some definitions for the squeezed displaced Fock states (SDFSs) are given. The hyperbolic analytic representation in the complex plane is considered. An analytic representation of the SU(1,1) Lie group is given and the representation in the unit disk based on the SU(1,1) PCSs for SDFSs is considered.      

Calculation of Berry's phase in squeezed states

A simple method based on generalized coherent states is proposed for calculation of Berry's phase. In this paper we calculate Berry's phase for a translated oscillator in standard coherent states as well as Berry's phase in squeezed states and spin coherent states, i.e., coherent states for the SU(1, 1) and SU(2) groups, respectively.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 51–59, 1988.     

Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum J. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from J to ${K=J+\frac{1}{2}, J+1, ... ,}$ with ${K=\infty}$ corresponding to the Wehrl map to classical densities. These channels were later recognized as the optimal quantum cloning channels. For each J and ${J < K \leqslant \infty}$ we show that the minimal output entropy for the channels occurs for a J coherent state. We also show that coherent states both Glauber and Bloch minimize any concave functional, not just entropy.     

Quantum random walk on the dual of SU (n)

Summary We study a quantum random walk onA(SU(n)), the von Neumann algebra of SU(n), obtained by tensoring the basic representation of SU(n). Two classical Markov chains are derived from this quantum random walk, by restriction to commutative subalgebras ofA(SU(n)), and the main result of the paper states that these two Markov chains are related by means of Doob'sh-processes.     

Quaternionic vector coherent states and the supersymmetric harmonic oscillator

The quaternionic vector coherent states are realized as coherent states of the supersymmetric harmonic oscillator with broken symmetry in analogy with the standard canonical coherent states of the ordinary harmonic oscillator. We study the nonclassical properties of the oscillator, such as the photon number distribution and signal-to-quantum-noise ratio in terms of these states and discuss the squeezing properties and the temporal stability of the coherent states. We obtain the orthogonal polynomials associated with the quaternionic vector coherent states. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 80–98, October, 2006.     

Coherent states for the Hartmann potential

We obtain the coherent states for a particle in the noncentral Hartmann potential by transforming the problem into four isotropic oscillators evolving in a parametric time. We use path integration over the holomorphic coordinates to find the quantum states for these oscillators. The decomposition of the transition amplitudes gives the coherent states and their parametric-time evolution for the particle in the Hartmann potential. We also derive the coherent states in the parabolic coordinates by considering the transition amplitudes between the coherent states and eigenstates in the configuration space. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 439–452, June, 2008.     

Charlier Polynomials and Charlier Oscillator as Discrete Realization of the Harmonic Oscillator

The Charlier polynomials are used for constructing oscillator-like systems. We introduce coherent states of the system are defined and study the main properties (in particular, the (over)completeness property). We show that the coherent states on the associated uncertainty relation take the minimum value. In the case under consideration, the Mandel parameter vanishes, which corresponds to the Poisson statistics of quasiexcitation spectrum for the considered oscillator. Bibliography: 30 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 3–15.     

Coherent States for the Legendre Oscillator

Two families of coherent states (the eigenstates of the annihilation operator and the Klauder–Gazeau temporally stable coherent states) are constructed for the Legendre oscillator defined in this paper. Bibliography: 14 titles.     

Generalized oscillator and its coherent states

We construct a system (a generalized oscillator) that is similar to the oscillator and is related to a system of orthogonal polynomials on the real axis. We define coherent states in the Fock space associated with the generalized oscillator. In the example of the generalized oscillator related to the Gegenbauer polynomials, we prove the (super)completeness of these coherent states, i.e., we construct a measure determining a partition of unity. We present a formula that allows calculating the Mandel parameter for the constructed coherent states. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 363–380, December, 2007.