The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical sys...

Basic computational aspects of the Wigner function approach for modeling and simulation of electronic transport are discussed, beginning with the coherent problem, followed by the dissipative problem including scattering events, which has been recently restated in terms of a scattering-induced Wigner function correction. These alternative formulations of the computational task are discussed alo...

Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It turns out that one may construct out of a pair of resonant states an analog of the stationary Wigner function.

The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is defined using the Newton-Wigner position operator. The perturbative solution for the time evolution is found. Causality is found to be perturbatively respected. 1 1 Introduction. The Wigner-Weyl formalism [1] offers a classical-like formulation...

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The information conveyed by the discrete Wigner-Ville representations of real, complex or analytic signals is highly redundant, each time-frequency location being related to others via non-obvious relationships. In this paper, we demonstrate that there also exists a large amount of linear relationships between time-frequency sample!;. This implies that a whole discrete Wigner-Ville representati...

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to ...

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decohere...

Heart sounds and murmurs are time-varying signals that would best be analyzed using time-frequency analysis. Windowed Wigner-Ville distribution (WWVD) and smooth windowed Wigner-Ville distribution (SWWVD) are used to obtain the timefiequency representation (TFR) of the signal. Determination of parameter setting of WWVD and SWWVD will eliminate the cross-terms and improve TFR. The accuracy of TF...