Related papers: Moyal Brackets, Star Products and the Generalised …
A full consideration of classical and quantum systems with radiation (electromagnetic/gravitational) requires the involvement of a mathematical description in the generalized phase space of high kinematical values. Based on the dispersion…
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…
Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
We study the Wigner functions of the nucleon which provide multidimensional images of the quark distributions in phase space and combine in a single picture all the information contained in the generalized parton distributions (GPDs) and…
A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators, which is a distribution uniquely characterized by the property that the marginals for all linear combinations of the given operators agree with the…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are deduced. The equations are valid for any solid,…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is…
The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the…
The quadratic nature of the Wigner distribution causes the appearance of unwanted interferences. This is the reason why engineers, mathematicians and physicists look for related time-frequency distributions, many of them are members of the…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be…