Related papers: Wigner Function Shapelets I : formalism
This paper describes the Wide Field Spectrograph (WiFeS) under construction at the Research School of Astronomy and Astrophysics (RSAA) of the Australian National University (ANU) for the ANU 2.3m telescope at the Siding Spring Observatory.…
Several types of Wavefront Sensors (WFS) are nowadays available in the field of Adaptive Optics (AO). Generally speaking, their basic principle consists in measuring slopes or curvatures of Wavefront Errors (WFE) transmitted by a telescope,…
The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic effects, which become important on large scales. At the same time, wide-angle (WA) effects due to differing…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
We present a method to simulate deep sky images, including realistic galaxy morphologies and telescope characteristics. To achieve a wide diversity of simulated galaxy morphologies, we first use the shapelets formalism to parametrize the…
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles…
Interactions between charged particles and light occur in real space and time, yet quantum field theory usually describes them in momentum space. Whereas this approach is well suited for calculating emission probabilities and cross…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We study the electroweak phase transition within a 5D warped model including a scalar potential with an exponential behavior, and strong back-reaction over the metric, in the infrared. By means of a novel treatment of the superpotential…
We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons…
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space…
Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…
The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on…
We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their…
In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore…
In this paper, we generalize the weighted Fourier transform with respect to a function, originally proposed for the one-dimensional case in \cite{Dorrego}, to the $n$-dimensional Euclidean space $\mathbb{R}^{n}$. We develop a comprehensive…
Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we…