We show the adaptation of a multifunctional optical system consisting of two spatial light modulators for the optimal measurement of the Radon-Wigner transform of one-dimensional signals. The proposed Radon-Wigner display allows reconstructing the Wigner distribution and the phase or the mutual intensity of fully or partially coherent fields, respectively. It is also suitable for the analysis o...

We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points.

We prove that for [ui,j ] n i,j=1 the eigenvectors matrix of a Wigner matrix, under some moments conditions, the bivariate random process BB@ X 1≤i≤ns, 1≤j≤nt (|ui,j | − 1/n) CCA (s,t)∈[0,1]2 converges in distribution to a bivariate Brownian bridge. This result has already been proved for GOE and GUE matrices. It is conjectured here that the necessary and sufficient condition, for the result to...

Zusammenfassung As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation that is, on the one hand, the formation of a second masterequation for the development of parameters, and, on the other hand, the use of the Wigner-distribution to describe the developmen...

The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form which is both concise and explicit. Since the conventional uncertainty principle is such a constraint on the first and second moments, our result constitutes a g...

We discuss important attributes of a discrete Wigner distribution derived using a group-theoretic approach. The nature of this approach enables this distribution to satisfy numerous mathematical properties, including marginals and the Weyl correspondence. A few issues concerning the relationship of this distribution with group theory are explored in detail. In particular , the discrete distribu...