Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

@article{Ginzburg2014TimeEO,
  title={Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.},
  author={David Ginzburg and Anke Mann},
  journal={Applied optics},
  year={2014},
  volume={53 8},
  pages={
          1648-57
        }
}
A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions. 
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