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… 
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Background Citations
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Methods Citations
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References

SHOWING 1-10 OF 20 REFERENCES

Wigner distribution function for paraxial polychromatic optics

The wigner distribution function and its optical production

Wigner distribution function display of complex 1D signals

Elements of euclidean optics

Euclidean optics are models of the manifold of rays and wavefronts in terms of coset spaces of the Euclidean group. One realization of this construction is the geometric model of Hamilton's optical…

On the Quantum Correction for Thermodynamic Equilibrium

The behavior of any system at high enough temperatures approaches that of its classical counterpart. The probability of any configurational position is then proportional to exp—U/kT, with U the…

Distribution functions in physics: Fundamentals

Invariant inner products on spaces of solutions of the Klein–Gordon and Helmholtz equations

We construct sesquilinear forms which are invariant under the similarity groups of the Klein–Gordon and Helmholtz equations. These give rise to positive definite inner products on subspaces of…

Representation of Lie groups and special functions

At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the…

Wigner distribution function for paraxial polychromatic optics Opt

  • Commun
  • 1997

Wigner distribution function for finite signals

We construct a bilinear form with the properties of the Wigner distribution function for a model of finite optics: the multimodal linear waveguide. This is a guide that can carry a finite number of…