The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates theWigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of WignerVille di...

A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decohere...

The Wigner-Eckart theorem concerns matrix elements of a type that is of frequent occurrence in all areas of quantum physics, especially in perturbation theory and in the theory of the emission and absorption of radiation. This theorem allows one to determine very quickly the selection rules for the matrix element that follow from rotational invariance. In addition, if matrix elements must be ca...

By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-fo...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

The Wigner rotation is important in many branches of physics, chemistry, and engineering sciences. It is a group theoretical effect resulting from two Lorentz boosts. The net effect is one boost followed or preceded by a rotation. While the term "Wigner rotation" is derived from Wigner's little group whose transformations leave the four-momentum of a given particle invariant, it is shown that t...

We study the competition between the Wigner crystal and the Laughlin liquid states in an ultracold quasi-two-dimensional rapidly rotating polarized fermionic dipolar gas, and find that the Wigner crystal has a lower energy below a critical filling factor. We examine the quantum crystal to liquid transition for different confinements in the third direction. Our analysis of the phonon spectra of ...

The on-axis intensity distribution, or the Strehl ratio versus defocus, is described in a phase-space domain in terms of the Wigner distribution function. A coordinate transformation that is defined for a general annular aperture is employed to convert the pupil amplitude transmittance into a one-dimensional function. We show that the single display of the Wigner distribution function associate...

A unified mathematical formulation for designing and analyzing even the most general optical processor is presented. It exploits the Wigner distribution function to characterize the illumination, the input, the inherent filter, and the output results. To characterize the propagation of the light through the optical processor setup, we exploit the Wigner matrix formalism, which is appealing beca...