Related papers: Quantum Distributions for the Plane Rotator
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 single electromagnetic plane-wave propagating in free space possesses neither spin nor orbital angular momentum. Both types of angular momentum arise from interference between pairs of plane-waves having the same temporal frequency…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type…
Definitions of orbital angular momentum based on Wigner distributions are used to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. The difference between these two…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the…
Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived,…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state $\vert \alpha,m \rangle$ due to a time--dependence of the frequency of the…
We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones.…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
The spin-dependent trial wave functions with rotational symmetry are introduced to describe rotating Wigner molecular states with spin degree of freedom in four- and five-electron quantum dots under magnetic fields. The functions are…
It is shown that the the quantum phase space distributions corresponding to a density operator $\rho$ can be expressed, in thermofield dynamics, as overlaps between the state $\mid \rho >$ and "thermal" coherent states. The usefulness of…
A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its…
For a quantum oscillator with the polynomial potential an explicit expression that describes the energy distribution as a coordinate (and momentum) function is obtained. The presence of the energy function poles is shown for the quantum…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…