Related papers: Wigner Distribution Functions and the Representati…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner…
The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$…
We describe radiative processes in Quantum Cosmology, from the solutions of the Wheeler De Witt equation. By virtue of this constraint equation, the quantum propagation of gravity is modified by the matter interaction hamiltonian at the…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
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…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z_N x Z_N with N odd. By introducing a phase factor extension to the phase…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
In this paper, we study the classical limit and unitary evolution of quantum cosmology by applying the Weyl--Wigner--Groenewold--Moyal formalism of deformation quantization to quantum cosmology of a homogeneous and isotropic universe with…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We develop the concept of quantum phase-space (Wigner) distributions for quarks and gluons in the proton. To appreciate their physical content, we analyze the contraints from special relativity on the interpretation of elastic form factors,…
We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship…
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example,…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative…