We introduce a τ -dependent Wigner representation, Wigτ , τ ∈ [0, 1], which permits us to define a general theory connecting time-frequency representations on one side and pseudo-differential operators on the other. The scheme includes various types of time-frequency representations, among the others the classical Wigner and Rihaczek representations and the most common classes of pseudo-differe...

We further elaborate on a phase-space picture for a system of N qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and different entanglement properties. We discuss the construction of discrete covariant Wigner functions for these bundles and provide several illuminating examples.

Many commonly used time–frequency distributions are members of the Cohen class. This class is defined for continuous signals, and since time–frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time–frequency distributions that are covariant to time shifts and frequency...

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/ √ t, for the energy current correlation in equil...

In the beginning of the 1950’s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the socalled Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. ...

The modulation-based time-variant filters are very useful for nonstationary signal processing. They can be constructed by three stages: pre-modulation, time-invariant low-pass filtering and post-modulation. Wigner distribution is a popular tool for showing the time-frequency distribution of nonstationary signals. The combination of these two techniques is presented in this paper. We introduce W...

We extend Hardy’s uncertainty principle for a square integrable function ψ and its Fourier transform to the n-dimensional case using a symplectic diagonalization. We use this extension to show that Hardy’s uncertainty principle is equivalent to a statement on the Wigner distribution Wψ of ψ. We give a geometric interpretation of our results in terms of the notion of symplectic capacity of an el...

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 derive transport theoretic boundary conditions for acoustic wave reflection at a weakly rough boundary in an inhomogeneous half space. We use the Wigner distribution to go from waves to energy transport in the high frequency limit. We generalize known results on the reflection of acoustic plane waves in a homogeneous medium. We analyze higher order corrections, which include a enhanced backs...