The Wigner distribution functions of coherent and partially coherent Bessel-Gaussian beams

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function,an analytical expression of the Wigner distribution function(WDF) for a coherent or partially coherent Bessel-Gaussian beam is presented.The reduced two-dimensional WDFs are also demonstrated graphically,which reveals the dependence of the reduced WDFs on the beam parameters.     

The Wigner distribution functions of coherent and partially coherent Bessel-Gaussian beams

Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel-Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.     

Classical divergence of nonlinear response functions

The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann distribution function. The implications of this study are discussed in the context of the conceptual development of quantum-classical correspondence in dynamic response.     

Phase-space representation of quantum systems in the relative-state formulation

A phase-space representation of quantum systems within the framework of the relative-state formulation is proposed. To this end, relative-position and relative-momentum states are introduced and their properties are investigated in detail. Phase-space functions that represent a quantum state vector are constructed in terms of the relative-positive and relative-momentum states, and the quantum dynamics is investigated by using the phase-space functions. Furthermore, probability distributions in phase space are considered by means of the relativestate formulation, and it is shown that the phase-space probability distribution is closely related to the operational probability distribution. The marginal distribution, characteristic function, and operational uncertainty relation are also discussed.     

Comment on “Why the `coarse-graining' of Wigner function is always coarse” [Opt. Commun. 178 (2000) 147]

Incorrect statements and assumptions undermining the validity of the results presented in the above paper are pointed out and shortly discussed. It is stressed that a proper `coarse graining' of a Wigner phase-space distribution function cannot be in general performed over finite phase-space cells and that any `smearing' over infinite phase-space areas cannot violate the respective uncertainty relations, which furnishes an answer to the question asked in the title.     

Measurement-induced decoherence and Gaussian smoothing of the Wigner distribution function

We study the problem of measurement-induced decoherence using the phase-space approach employing the Gaussian-smoothed Wigner distribution function. Our investigation is based on the notion that measurement-induced decoherence is represented by the transition from the Wigner distribution to the Gaussian-smoothed Wigner distribution with the widths of the smoothing function identified as measurement errors. We also compare the smoothed Wigner distribution with the corresponding distribution resulting from the classical analysis. The distributions we computed are the phase-space distributions for simple one-dimensional dynamical systems such as a particle in a square-well potential and a particle moving under the influence of a step potential, and the time-frequency distributions for high-harmonic radiation emitted from an atom irradiated by short, intense laser pulses.     

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar. Received 28 March 2000     

The impulse response function of apertured and misaligned ABCD optical system in phase-space

By expanding the aperture into complex Gaussian functions, the approximate analytical impulse response function of apertured and misaligned ABCD optical system in phase-space is determined, which allows us to formulate the input-output relation completely in terms of Wigner distribution functions. Its shown that the hard-aperture placed before the optical system will change the shape of output signal Wigner distribution and the misalignment of optical system will introduce the output Wigner distribution function a coordinate shift in phase-space. For examining the analytical results some numerical simulation are done and the graphical results as well as the absolute errors between analytical results and numerical integral ones are presented.     

Linear canonical Wigner distribution and its application

Linear canonical transform (LCT) form a three-parameter family of intergral transforms with wide application in optics. In this paper, we investigate the linear canonical Wigner distribution (LCWD) which is based on the LCT and the classical Wigner distribution (WD). Firstly, the definition of LCWD is discussed. Moreover, the transformation law for the LCWD through a first-order optical system is derived. This new phase-space distribution provides analysis of signals in both space and LCT domains simultaneously. Then, the main properties of LCWD are investigated in detail. Finally, the application of the LCWD is presented. The LCWD is found to be the appropriate phase-space distribution function for light-beam characterization in first-order optical system. Moreover, the moment matrix formalism for beam characterization is studied.     

Machine failure forewarning via phase-space dissimilarity measures

We present a model-independent, data-driven approach to quantify dynamical changes in nonlinear, possibly chaotic, processes with application to machine failure forewarning. From time-windowed data sets, we use time-delay phase-space reconstruction to obtain a discrete form of the invariant distribution function on the attractor. Condition change in the system's dynamic is quantified by dissimilarity measures of the difference between the test case and baseline distribution functions. We analyze time-serial mechanical (vibration) power data from several large motor-driven systems with accelerated failures and seeded faults. The phase-space dissimilarity measures show a higher consistency and discriminating power than traditional statistical and nonlinear measures, which warrants their use for timely forewarning of equipment failure.     

Energy- andN-averagings in the shell correction method

It is shown that a difference exists between the mean values of the total single-particle energies obtained by averaging over the nucleon numberN and over the phase-space distributions (the energy-averaging) due to the symmetry of the single-particle Hamiltonian. This difference could lead to significant corrections in fitting the nuclear masses involving the droplet model.     

Experimental Technique to Measure Phase-Space Diagrams in Plasma Experiments

An experimental technique is described which allows one to easily measure and rapidly display the particle distribution function in phase-space in nonlinear wave-plasma interaction experiments. An application to the study of Pseudowaves is also presented.     

High Unloaded Qs MM Wave WDR Filters Designing

The designing results of original high unloaded-Q waveguide-dielectric filters (WDFs), are discussed. The basic physical ideas, underlying the unique design of both narrow- and wide-band filters with a widened region of suppression up to a doubled working frequency and higher, with low losses (0.2-0.5 dB), are set forth; some of their parameters in the frequency range from 8 GHz up to 80 GHz, are brought forward. The distinctive features of a WDFs are observed and the perspective directions of their development and application are predicted.     

Husimi Function of Excited Squeezed Vacuum State

The q-p phase-space distribution function is a popular tool to study semiclassical physics and to describe the quantum aspects of a system. In this paper by using the pure state density operator formula of the Husimi operator Δ_h(q,p;κ)=|p,q〉_κκ〈p,q| we deduce the Husimi function of the excited squeezed vacuum state. Then we study the behavior of Husimi distribution graphically.     

On constructing the wave function of a quantum particle from its Wigner phase-space distribution function

For a Schrödinger wave function, the part of the phase that depends only on time disappears in the construction of the corresponding Wigner phase-space (quasi)distribution function. Despite this, it can be recovered from the Wigner function using the quantum Hamilton–Jacobi equation. This is demonstrated for three simple cases.     

Operational Phase-Space Probability Distribution in Quantum Communication Theory

Operational phase-space probability distributions are useful tools for describing quantum mechanical systems, including quantum communication and quantum information processing systems. It is shown that quantum communication channels with Gaussian noise and quantum teleportation of continuous variables are described by operational phase-space probability distributions. The relation of operational phase-space probability distribution to the extended phase-space formalism proposed by Chountasis and Vourdas is discussed.     

On marginalization of phase-space distribution functions

We discuss marginalization procedures based on integration of quantum phase-space distribution functions over a family of phase-space manifolds. We show that under some conditions the resulting marginals are always nonnegative.     

中心快度区的双轻子不变质量分布

推广先前作者采用的夸克和π的相空间分布函数的Boltzmann近似到一个完全的表示,利用快度区的温度计算出粒子密度后,在Bjorken的(1+1)维的纵向膨胀系统中研究了双轻子的产生.发现推广的近似分布函数很大地改变了预言的夸克物质形成的特征双轻子分布.