Sampling theorem and the number of degrees of freedom of an image

A sampling theorem in a form suitable for coherent optical signals transmitted by an optical system with circular aperture is presented. The theorem is used to calculate the degrees of freedom of an image if the optical system has a disk or a ring aperture.     

Quantum mechanical version of the classical Liouville theorem

In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from |z>to|sz-rz*> corresponds to the motion from a point z(q,p) to another point sz-rz* with |s|2-|r|2=1.The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics.     

SORE APPLICATIONS OF THE COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

On the basis of the preceding paper^[1]we present some new applications of both the normal rroduct form and the coherent state form of the Wigner operator,which involve deriving some new quantum operator formulas, giving the coherent state generalization of the Moyal theorem, evaluating some quantum operators which correspond to the given classical functions in the weyl manner and vice versa. Were it not for the Wigner operator's coherent state formulation given by us the above-mentioned calculations would be hard to perform.     

Quanta and coherent states

The quantum harmonic oscillator can be considered as a composite system of indistinguishable Bose-Einstein symmetric two-level-systems (quanta). In analogy to the classical Poisson limit theorem, we show that a coherent state is the limit of a sequence of homogeneous product states (coherent spin states) and discuss statistical properties of the quanta in classical and nonclassical states.     

SOME APPLICATIONS OF COHERENT STATE FORMULATION OF THE WIGNER OPERATOR

In this paper both the normal product form and the coherent state form of the Wigner operator are derived. Furthermore, the applications of the new forms of the Wigner operator are also presented, which are involved in deriving some new quantum operator formulas, in the coherent state generalization of the Moyal theorem, and in evaluating some quantum operators which corresponds to the given classical functions in the Weyl manner and vice versa.     

Quantum mechanical version of classical Liouville theorem

In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of coherent state from |z〉to |sz-rz^*〉angle corresponds to the motion from a point z(q,p) to another point sz-rz^* with |s|²-|r|²=1. The evolution is governed by the so-called Fresnel operator U(s,r) recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation and obeys the group product rules. In another word, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.     

Quantum optical ABCD theorem in two-mode case

By introducing the entangled Fresnel operator （EFO） this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics. The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO＇s normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators.     

Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied. Finally, using the Gazeau-Klauder coherent states approach, the time evolution of some of the nonclassical properties of the coherent states corresponding to the considered physical systems are discussed.     

Applications of the coherent state representation in the theory of magnetism: II. Helical spin configurations

In a previous paper, the coherent state representation of spin wave states was used to derive the low temperature expansion for the free energy of the Heisenberg model of a ferromagnet. In this paper, the same formalism is applied to anisotropic systems which are usually described semiclassically. The coherent state parameters are shown to be ideally suited for describing certain of the resulting helical spin configurations. The coherent state approach emphasizes the analogy of these states to superfluid boson systems. A model spin Hamiltonian appropriate to Erbium is chosen and discussed in this light. In particular, the transition in a transverse magnetic field from the ground state cone configuration to a fan configuration, the stability and possible metastability of these states and the fluctuations about them are investigated. Numerical estimates show at least qualitative agreement with experiment.     

Coherent state path integral methods and central limit theorem

We consider a coherent state path integral expression originating for example after path integration over a second interacting system and by using a method based on the use of the central limit theorem on the phase of the path integral representation, we extract under certain conditions a closed form for the propagator.     

Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.     

Coherent structure analysis of spatiotemporal chaos

We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence. The coherent structure decomposition is also used to define an entropy measure, which sharply increases in these systems at the transition to turbulence.     

Condensation in Hamiltonian parametric wave interaction

In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states. This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the H theorem of entropy growth inherent to the random phase approximation approach. The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping. As a result, the lower the coherence of the initial state, the higher the coherence of the final state.     

QUANTUM THEORY FOR FERMION SYSTEM AND ITS PSEUDO-CLASSICAL CORRESPONDENCE

On the basis of the fermionic coherent state formulation we propose the weyl-McCoy correspondence for fermion system, from which a functional integral form without the boundary term is derived. Moreover, the generating functional, the wigner theorem. and the Moyal bracket for fermion system are also demonstrated. Thus the theory of quantum mechanics for Fermi operators and its pseudo-classical correspondence is established.     

Macroscopic atom-molecule dark state and its collective excitations in fermionic systems

We show that a robust macroscopic atom-molecule dark state can exist in fermionic systems, which represents a coherent superposition between the ground molecular Bose-Einstein condensates and the atomic BCS paired state. We take advantage of the tunability offered by external laser fields, and explore this superposition for demonstrating coherent oscillations between ground molecules and atom pairs. We interpret the oscillation frequencies in terms of the collective excitations of the dark state.     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.     

Sources of arbitrary states of coherence that generate completely coherent fields outside the source

A new theorem concerning nonradiating stochastic sources is derived. The theorem is used to describe sources that can have a variety of different states of coherence and yet each of them generating a field that is completely spatially coherent outside the source domain. The bearing of this result on a basic unsolved problem is spectroscopy of partially coherent sources is noted.     

基于纠缠态表象和自旋相干态的新复变函数空间

本文利用有序算符内的积分(IWOP)技术,构造了一个基于单变量厄米多项式H2j(ξ*+τξ/2√τ)的新复变函数空间,该空间与纠缠态表象及施温格玻色环境下的自旋相干态有关。推导出了包含二元厄米多项式的二项式定理,有助于构造新的复变函数空间。同时还提出了一种新的基于H2j(ξ*+τξ/2√τ)的积分变换及其逆变换,这对于推导某些算符恒等式是很有用的。     

Enhancing the capability of controlling quantum systems via ancillary systems

This paper explores the potential of controlling quantum systems by introducing ancillary systems and then performing unitary operation on the resulting composite systems. It generalizes the concept of pure state controllability for quantum systems and establishes the link between the operator controllability of the composite system and the generalized pure state controllability of its subsystem. It is constructively demonstrated that if a composite quantum system can be transferred between any pair of orthonormal pure vectors, then its subsystem is generalized pure-state controllable. Furthermore, the unitary operation and the coherent control can be concretely given to transfer the system from an initial state to the target state. Therefore, these properties may be potentially applied in quantum information, such as manipulating multiple quantum bits and creating entangled pure states. A concrete example has been given to illustrate that a maximally entangled pure state of a quantum system can be generated by introducing an ancillary system and performing open-loop coherent control on the resulting composite system.     

Bounded coherent states and excitonic systems

New bounded coherent state construction, based in a Keldysh conjecture, is presented. The particular group structure arising from the model leads a new symmetry transformations for the coherent state system. The emergent new symmetry transformations are reminiscent of the Bogoliubov ones. This construction is applied to describe an excitonic system. We discuss how the symmetry of these transformations is intrinsically related with the stability and the behavior of the physical systems as in the excitonic case.