Related papers: Wigner distributions for finite dimensional quantu…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics…
A mapping between operators on the Hilbert space of $N$-dimensional quantum system and the Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed…
We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values,…
Leveraging an algebraic approach built on minimal realizations and conditional expectations in quantum probability, we propose a method to reduce the dimension of quantum filters in discrete-time, while maintaining the correct distributions…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
The use of the Wigner function for the study of quantum transport in open systems present severe criticisms. Some of the problems arise from the assumption of infinite coherence length of the electron dynamics outside the system of…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\bf R}_A$ and ${\bf P}_A,\; A=1,\ldots,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
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…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
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…