The on-axis image irradiance obtained from a radially symmetric optical system under broadband illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying on-axis irradiance can be derived from different slices of a two-dimensi...

We study Wigner function value statistics of classically chaotic quantum maps on compact 2D phase space. We show that the Wigner function statistics of a random state is a Gaussian, with the mean value becoming negligible compared to the width in the semiclassical limit. Using numerical example of quantized sawtooth map we demonstrate that the relaxation of time-dependent Wigner function statis...

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicityfree) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix...

We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state. The Wigner function provides a complete representation of the quantum state in the form that is analogous to a c...

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigne...

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion i...

Wigner function(WF), a quasi-probability distribution in phase space, was first introduced to describe quantum state in quantum mechanics by E. P. Wigner[1]. And later, it was extended to classical optics and signal processing. Since its birth, a great number of applications have been conducted in different fields. As for the original quantum case, like a continuous onedimensional quantum syste...