# Wigner distribution function for Euclidean systems

@inproceedings{Nieto1997WignerDF, title={Wigner distribution function for Euclidean systems}, author={Luis Miguel Nieto and Natig M. Atakishiyev and Sergey M. Chumakov}, year={1997} }

Euclidean systems include poly- and monochromatic wide-angle optics, acoustics, and also infinite discrete data sets. We use a recently defined Wigner operator and (quasiprobability) distribution function to set up and study the phase-space evolution of these models, subject to differential and difference equations, respectively. Infinite data sets and two- dimensional monochromatic (Helmholtz) fields are thus shown by their Wigner function on a cylinder of (2 ) direction and location; the…

## 38 Citations

Position and momentum bases for the monochromatic Maxwell fish-eye and the sphere

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In geometric optics the Maxwell fish-eye is a medium where light rays follow circles, while in scalar wave optics this medium can only ‘trap’ fields of certain discrete frequencies. In the…

Wigner functions for Helmholtz wave fields

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We investigate a general form of the Wigner function for wave fields that satisfy the Helmholtz equation in two-dimensional free space. The momentum moment of this Wigner function is shown to…

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We construct and analyze a Hamiltonian system whose position coordinate takes values on the finite subset of contiguous integers Zj := {−j,−j+1, . . . , j}, with the purpose of applying the resulting…

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- 2008

In geometric optics there is a natural distinction between the paraxial and aberration regimes, which contain respectively the linear and nonlinear canonical transformations of position and momentum…

Finite optical Hamiltonian systems

- PhysicsInternational Commission for Optics
- 2011

In this essay we finitely quantize the Hamiltonian system of geometric optics to a finite system that is also Hamiltonian, but where signals are described by complex N-vectors, which are subject to…

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- PhysicsQuantum
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This work derives in a consistent way a Wigner distribution for SU(1,1), which appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it.

Finite signals in planar waveguides.

- PhysicsJournal of the Optical Society of America. A, Optics, image science, and vision
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The Kravchuk coherent states provided by the finite oscillator model are used to evince the nonlinear transformations that elliptic-profile waveguides produce on phase space by means of the SO(3) Wigner function.

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We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar…

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For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, and , provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in…

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