Related papers: A Wigner distribution function for finite oscillat…
Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice ${\ee Z}_{D} \times {\ee Z}_{D}$ with specific emphasis on the deformed oscillator subalgebras and the generalized representations…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)_{\alpha}. This algebra is a deformation of the Lie algebra u(2) extended by a parity operator, with deformation parameter {\alpha}. A…
Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…
For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…
The mapping of the Wigner distribution function (WDF) for a given bound-state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse…
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and momentum operators of the oscillator as odd elements of the Lie…
Expressing the Wigner distribution function in Dirac notation reveals its resemblance to a classical trajectory in phase space.
The quasi-probabilistic Wigner distributions are the quantum mechanical analog of the classical phase-space distributions. We investigate quark Wigner distributions for a quark state dressed with a gluon, which can be thought of as a simple…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
A relativistic Wigner function for free Discrete Time Quantum Walks (DTQWs) on the square $2D$ space-time lattice is defined. Useful concepts such as discrete derivatives and discrete distributions are also introduced. The transport…
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the…
We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the…
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…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
We analyze a known version of the discrete Wigner function and some connections with Quantum Iterated Funcion Systems. This paper is a follow up of "A dynamical point of view of Quantum Information: entropy and pressure" by the same…
We consider the Wigner quasi-probability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex…
Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous…
It is shown that the number-phase Wigner function defines uniquely the respective density operator. Relations between the Glauber-Sudarshan distribution $\mathcal{P}(\alpha)$ and the number-phase Wigner function is found. This result is…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…