Related papers: Wigner function for SU(1,1)
This paper studies one-loop effective potential and spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter space-time. Curvature effects modify the flat-space effective potential by means of a very complicated special…
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…
The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…
Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the…
A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and $\tau$-Wigner distributions, using metaplectic operators. However, in order for a metaplectic…
The Schr\"odinger equation in phase space is used to calculate the Wigner function for the Helium atom in the approximation of a system of two oscillators. Dissipation effect is analysed and the non-classicality of the state is studied by…
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen…
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation…
For the stationary Wigner equation with inflow boundary conditions, its numerical convergence with respect to the velocity mesh size are deteriorated due to the singularity at velocity zero. In this paper, using the fact that the solution…
A theory of joint nonideal measurement of incompatible observables is used in order to assess the relative merits of quantum tomography and certain measurements of generalized observables, with respect to completeness of the obtained…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
In a recent paper [PRE 62, 4665 (2000)] (quant-ph/0203102) Manfredi and Feix proposed an alternative definition of quantum entropy based on Wigner phase-space distribution functions and discussed its properties. They proposed also some…
Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It…
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
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…
The SU(2) Wigner function represents a quantum state of a spin-$J$ as a real-valued function on the surface of a 2-sphere. For an ensemble of $N$ spin-1/2 particles, this representation is useful when the dynamics is restricted to a single…