It is shown that Bell’s proof of violation of local realism in phase space is incorrect. Using Bell’s approach, a violation can be derived also for nonnegative Wigner distributions. The error is found to lie in the use of an unnormalizable Wigner function.

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

Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration in the frequency domain allows the determination of near-field diffraction, leading to the well known Fresnel diffraction when small angles are considered an...

The generalized optical transfer function and the spectral correlation function are investigated for nonparaxial two-dimensional wave fields. The angle-impact marginal of the four-dimensional Wigner function is derived directly. For focused wave fields of semiangle greater than 90 degrees, the spectral correlation function exhibits overlapping and interference. For focused wave fields for which...

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability di...

We discuss the problem of finding ”marginal” distributions within different tomographic approaches to quantum state measurement, and we establish analytical connections among them. PACS number(s): 03.65.-w, 42.50.-p

We demonstrate the ability of the phase space formulation of quantum mechanics to provide convenient means and intuitive notions for exploring the process of transition from a quantum to a classical state known as decoherence. The Wigner equation, which is usually relevant for electron transport in nanostructures, augmented by the Boltzmann scattering operator is now applied to the time depende...

We have studied statistical properties of the values of the Wigner function W (x) of 1D quantum maps on compact 2D phase space of finite area V . For this purpose we have defined a Wigner function probability distribution P (w) = (1/V ) ∫ δ(w − W (x))dx, which has, by definition, fixed first and second moment. In particular, we concentrate on relaxation of time evolving quantum state in terms o...

Cross-terms lie between two auto-components and are oscillatory, with their frequencies increasing with increasing distance in time-frequency between the two components. The cross-terms can have a peak value as high as twice that of the auto-components. A Wigner distribution of a two-component signal is shown in Figure 1. In this figure, it is easy to separate the auto-components from the cross...