Relations between classical phase-space distributions and Wigner functions for multiparticle production processes. Abstract The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production , are discussed. The temperature for the classical description is always higher than that for its Wigner function interpretation. A ro...

We propose a new method for analysis of the sampling and reconstruction conditions of real and complex signals by use of the Wigner domain. It is shown that the Wigner domain may provide a better understanding of the sampling process than the traditional Fourier domain. For example, it explains how certain non-bandlimited complex functions can be sampled and perfectly reconstructed. On the basi...

Applying the fractional Fourier transform and the Wigner distribution on a signal in a cascade fashion is equivalent with a rotation of the time and frequency parameters of the Wigner distribution. This report presents a formula for all unitary operators that are related to energy preserving transformations on the parameters of the Wigner distribution by means of such a cascade of operators. Fu...

I. Abstract Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over nonco...

We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.

We consider the space-time Wigner transform of the solution of the random Schrödinger equation in the white noise limit and for high frequencies. We analyze in particular the strong lateral diversity limit in which the space-time Wigner transform becomes weakly deterministic. We also show how to use these asymptotic results in broadband array imaging in random media.

We characterize the Schwartz space of rapidly decaying test functions by the decay of the short-time Fourier transform or cross-Wigner distribution. Then we prove a version of Hardy’s theorem for the short-time Fourier transform and for the Wigner distribution.

In the rotation based fast multipole method the accurate determination of the Wigner rotation matrices is essential. The combination of two recurrence relations and the control of the error accumulations allow a very precise determination of the Wigner rotation matrices. The recurrence formulas are simple, efficient, and numerically stable. The advantages over other recursions are documented.

WIGNER HIGH-ELECTRON-CORRELATION REGIME OF NON-UNIFORM DENSITY SYSTEMS: A QUANTAL-DENSITY-FUNCTIONAL-THEORY STUDY by DOUGLAS M. ACHAN Advisor: Prof. Lou Massa The Wigner regime of a system of electrons in an external field is characterized by a low electron density and a high electron-interaction energy relative to the kinetic energy. The low correlation regime is in turn described by a high el...