Related papers: Mutual space-frequency distribution of Gaussian si…
CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
In this paper we develop a new technique to model joint distributions of signals. Our technique is based on quantum mechanical conjugate variables. We show that the transition probability of quantum states leads to a distance function on…
The present note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting…
A system of coupled kinetic transport equations for the Wigner distributions of a free variable mass Klein-Gordon field is derived. This set of equations is formally equivalent to the full wave equation for electromagnetic waves in…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial…
We study the propagation of high-frequency electromagnetic waves in randomly heterogeneous bianisotropic media with dissipative properties. For that purpose we consider randomly fluctuating optical responses of such media with correlation…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
We study the gluon Wigner distributions of the proton which are the phase-space distributions containing the most general one-parton information. Using the proton wave functions deduced from a light-cone spectator model that contains the…
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is…
The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
This note presents a rigorous introduction to a selection of distributions along with their Fourier transforms, which are commonly encountered in signal processing and, in particular, magnetic resonance imaging (MRI). In contrast to many…
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…
A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…
The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of…
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…
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…