有限维希尔伯特空间非简谐振子广义相干态

在有限维希尔伯特空间中构造了非简谐振子的广义相干态,并研究了其量子统计特性。详细地讨论了该量子态的压缩效应和反聚束效应,得到了出现压缩的条件并给陋了反聚束效应与有限维希尔伯特空间维数关系的数值计算结果。理论计算表明该量子态存在压缩效应和反聚束效应,这与通常的无限维空间中的广义相干态是完全不同的。     

Barut-Girardello Coherent States for the Parabolic Cylinder Functions

The Barut-Girardello coherent states for the parabolic cylinder functions are constructed. It is shown that the resolution of unity condition is satisfied for the coherent states. In the Hilbert space spanned by the parabolic cylinder eigenstates, the appropriate measure is also obtained.     

Generalized Klauder–Perelomov and Gazeau–Klauder coherent states for Landau levels

Based on a pair of representations obtained for Lie algebra h₄, the Hilbert space corresponding to all quantum states of Landau levels is split into an infinite direct sum of infinite-dimensional Hilbert subspaces. For any one of the Hilbert subspaces, we get linear combinations of their bases as generalized coherent states—the so-called Klauder–Perelomov and Gazeau–Klauder.     

有限维Hilbert空间一种新的奇偶非线性相干态

利用数值计算方法,研究了有限维Hilbert空间一种新的奇偶非线性相干态的反聚束效应.研究结果表明:各有限维Hilbert空间新的偶非线性相干态均不出现反聚束效应.但各有限维Hilbert空间新的奇非线性相干态均可出现反聚束效应.     

Variance Measure of Coherence of Quantum Pure States

We provide an expression for the measure of coherence of quantum pure states, which is obtained by quantifying the deviation or distance between the measured state and the maximally coherent states in the same Hilbert space. We classify quantum pure states in a Hilbert space according to their coherence and prove that the variance measure of coherence is proper for all quantum pure states. We demonstrate that the variance measure of coherence is simpler and easier to obtain than the l₁-norm of coherence and the relative entropy of coherence.

     

On nonlinear coherent states properties for electron-phonon dynamics

This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to an electron-phonon model in the condensed matter physics, obeying a f-deformed Heisenberg algebra. The existence and properties of reproducing kernel in the NCS Hilbert space are studied and discussed; the probability density and its dynamics in the basis of constructed coherent states are provided. A Glauber-Sudarshan P-representation of the density matrix and relevant issues related to the reproducing kernel properties are presented. Moreover, a NCS quantization of classical phase space observables is performed and illustrated in a concrete example of q-deformed coherent states. Finally, an exposition of quantum optical properties is given.     

有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

构造出了有限维Hilbert空间Roy型奇偶非线性相干态, 讨论了它们的正交归一完备性和振幅平方压缩效应. 研究表明, 在此空间中Roy型奇偶非线性相干态是归一完备的, 但不具有正交性; 当复参数相位角θ满足一定条件时它们存在振幅平方压缩效应, 同时导出了压缩条件与参数s,r以及函数f(n)之间的关系. 最后借助于数值计算, 发现对于5维(或7维)Hilbert空间中Roy型偶(或奇)非线性相干态, 当参数θ和Lamb-Dike参数η取某一给定值时, 在参数r变化的不同取值范围内, 它们均可以呈现振幅平方 关键词： 有限维Hilbert空间 Roy型非线性相干态 奇偶非线性相干态 振幅平方压缩     

有限维希尔伯特空间含时谐振子的时间演化及Berry相位

研究了有限维希尔伯特空间含时谐振子的时间演化．通过适当的含时规范变换得到有限维含时谐振子量子态时间演化的封闭解,并给出量子态的Ｂｅｒｒｙ相位．最后讨论了驱动项对相干态压缩特性的影响 关键词：     

Coherent states of potentials of soliton origin

The spectral properties of the most general time-dependent potentials of the soliton type described by a self-adjoint operator acting in Hilbert space are discussed. The spectral decomposition for these potentials and the quasispectral decomposition for the Darboux transformation operators are obtained. The coherent states of such systems are examined. Finally, the measure realizing the decomposition of the identity operator in the projectors on the coherent states is calculated. Zh. éksp. Teor. Fiz. 114, 1930–1943 (December 1998)     

A New Kind of k-Quantum Nonlinear Coherent States: Their Generation and Physical Meaning

A new kind of k-quantum nonlinear coherent states, i.e., the k eigenstates of the k-th power $\hat{B}^{k}$ (k≥3) of the generalized annihilation operator $\hat{B}=\hat{a}\frac1{f(\hat{N})}$ of f-oscillators, are obtained and their properties are discussed. The completeness of the k states is investigated. An alternative method to construct them is proposed. It is shown that these states may form a complete Hilbert space, and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states. Physically, they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.     

有限维希尔伯特空间q-畸变谐振子偶相干态及其压缩和反聚束特性

从一般形式上构造了有限维希尔伯特（Ｈｉｌｂｅｒｔ）空间ｑ－畸变谐振子的偶相干态,并讨论了其量子统计特性。发现有限维希尔伯特空间的偶ｑ－相干态与通常无限维空间的偶ｑ－相干态或偶相干态有明显不同的压缩和反聚束特性。前者的偶ｑ－相干态不仅出现正交压缩,而且出现反聚束效应。     

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.     

Coherent states of nonstationary soliton potentials

With the help of a nonstationary Darboux transformation, we have obtained a system of coherent states for the potential which is a solution of the Kadomtsev-Petviashvili equation. We have determined the measure realizing expansion of unity with respect to these states. We have constructed a holomorphic representation of the state vectors and the ladder operators for the discrete basis of the Hilbert space of solutions of the Schrödinger equation.     

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. 关键词： 非谐振子 Gazeau-Klauder相干态 Klauder-Perelomov相干态     

有限维希尔伯特空间中的非线性相干态

在有限维希尔伯特空间中构造了非线性相干态,并研究了该量子态的压缩效应和反聚束效应,给出了压缩效应和反聚束效应与有限维希尔伯特空间维数关系的数值计算结果.     

Relativistic Gamow Vectors

Whereas in Dirac quantum mechanics and relativistic quantum field theory one uses Schwartz space distributions, the extensions of the Hilbert space that we propose uses Hardy spaces. The in- and out-Lippmann-Schwinger kets of scattering theory are functionals in two rigged Hilbert space extensions of the same Hilbert space. This hypothesis also allows to introduce generalized vectors corresponding to unstable states, the Gamow kets. Here the relativistic formulation of the theory of unstable states is presented. It is shown that the relativistic Gamow vectors of the unstable states, defined by a resonance pole of the S-matrix, are classified according to the irreducible representations of the semigroup of the Poincaré transformations (into the forward light cone). As an application the problem of the mass definition of the intermediate vector boson Z is discussed and it is argued that only one mass definition leads to the exponential decay law, and that is not the standard definition of the on-the-mass-shell renormalization scheme.     

Coherent state map quantization in a Hermitian-like setting

For vector bundles having an involution on the base space, Hermitian-like structures are defined in terms of such an involution. We prove a universality theorem for suitable self-involutive reproducing kernels on Hermitian-like vector bundles. This result relies on pullback operations involving the tautological bundle on the Grassmann manifold of a Hilbert space and exhibits the aforementioned reproducing kernels as pullbacks of universal reproducing kernels that live on the Hermitian-like tautological bundle. To this end we use a certain type of classifying morphisms, which are geometric versions of the coherent state maps from quantum theory. As a consequence of that theorem, we obtain some differential geometric properties of these reproducing kernels in this setting.     

Coherent States with Complex Functions

The canonical coherent states are infinite series in powers of a complex number z. We present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions, and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states.     

Q变形非简谐振子广义奇偶相干态的高阶压缩特性

给出了Q变形的非简谐振子广义奇偶相干态的完备性证明,并且研究了它们的高阶压缩特性.结果表明,它们可组成一个完备的Hilbert空间,且均可呈现奇数阶压缩效应.     

Higher-Order Squeezing for Generalized Odd and Even Coherent States of a Q-Deformed Non-harmonic Oscillator

The completeness and higher-order squeezing properties of generalized odd and even coherent states of a Q-deformed non-harmonic oscillator are investigated. The results show that they may form a complete Hilbert space, and the odd-order squeezing effects exist in all of the states.