相关论文: Phase-space descriptions of operators and the Wign…

The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…

We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int…

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…

We advance a phase-space theory of partially coherent accelerating, non-diffracting beams employing the Wigner distribution function (WDF). We derive a general expression for the WDF of any accelerating, diffraction-free beam of arbitrary…

We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e.…

We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak…

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…

The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…

We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically…

We provide an introduction into the formulation of non-relativistic quantum mechanics using the Wigner phase-space distribution function and apply this concept to two physical situations at the interface of quantum theory and general…

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…

The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar…

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…

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 quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…

We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…

In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…

In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent…