Related papers: Wigner Function Shapelets I : formalism

We formulate, with full generality, the asymptotic estimation theory for Gaussian states in terms of their first and second moments. By expressing the quantum Fisher information (QFI) and the elusive symmetric logarithmic derivative (SLD)…

By means of a new mod(N)-invariant operator basis, s-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and…

We present the wavelength calibration for the lenslet-based Integral Field Spectrograph (IFS) that serves as the science instrument for the Gemini Planet Imager (GPI). The GPI IFS features a 2.7" x 2.7" field of view and a 190 x 190 lenslet…

The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by K.…

In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the introduction of (quasi-)algebras of Fourier integral…

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…

Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…

Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki --…

Undulator radiation from synchrotron light sources must be transported down a beamline from the source to the sample. A partially coherent photon beam may be represented in phase space using a Wigner function, and its transport may use some…

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions…

The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…

We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…

The use of Wavefront Sensors (WFS) is nowadays fundamental in the field of instrumental optics. This paper discusses the principle of an original and recently proposed new class of WFS. Their principle consists in evaluating the slopes of…

We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be…

In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…

We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry, are analogous to the n-point functions in…

For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…

The ingot wavefront sensor (I-WFS) has been proposed, for ELT-like apertures, as a possible pupil plane WFS, to cope with the geometrical characteristics of a laser guide star (LGS). Within the study and development of such a WFS, on-going…

We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…