Related papers: Generating All Wigner Functions
Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The…
We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectatnion operator. This allows to study discrete processes in free-measure setting. In…
Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…
A closed expression is given for the generating function of (virtual) Poincar\'e polynomials of moduli spaces of semi-stable sheaves on the projective plane $\mathbb{P}^2$ with arbitrary rank $r$ and Chern classes. This generating function…
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…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main…
Heralding, which is often used for preparing quantum optical states, is studied to determine the effects of the spatiotemporal properties of the process. Incorporating all the spatiotemporal degrees of freedom, we follow a Wigner functional…
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…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase…
For any state in a $D$-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function…
The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…