Related papers: Unifying distribution functions: some lesser known…
The cross-Wigner distribution $W(f,g)$ of two functions or temperate distributions $f,g$ is a fundamental tool in quantum mechanics and in signal analysis. Usually, in applications in time-frequency analysis $f$ and $g$ belong to some…
We use, for the first time, ab initio coupled-cluster theory to compute the spectral function of the uniform electron gas at a Wigner-Seitz radius of $r_\mathrm{s}=4$. The coupled-cluster approximations we employ go significantly beyond the…
The notion of brightness is efficiently conveyed in geometric optics as density of rays in phase space. Wigner has introduced his famous distribution in quantum mechanics as a quasi-probability density of a quantum system in phase space.…
For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner…
Wigner-type distributions have shown their effectiveness in classification problems of sonar and radar. We present an overview of applications where resonance features in echoes scattered from targets insonified or illuminated with short…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator…
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
This paper proposes to unify fading distributions by modeling the magnitude-squared of the instantaneous channel gain as an infinitely divisible random variable. A random variable is said to be infinitely divisible, if it can be written as…
The Wigner-Weyl- Moyal approach to Quantum Mechanics is recalled, and similarities to classical probability theory emphasised. The Wigner distribution function is generalised and viewed as a construction of a bosonic object, a target space…
The Wigner function was introduced as an attempt to describe quantum-mechanical fields with the tools inherited from classical statistical mechanics. In particular, it is widely used to describe the properties of radiation fields. In fact,…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
The break-by-one gamma distribution has a probability density function resembling the Schechter function, but with the small-argument behavior modified so it is normalizable in commonly arising cases where the Schechter function is not. Its…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution…