Related papers: Region Operators of Wigner Function: Transformatio…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable…
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 investigate operator algebraic origins of the classical Koopman-von Neumann wave function $\psi_{KvN}$ as well as the quantum mechanical one $\psi_{QM}$. We introduce a formalism of Operator Mechanics (OM) based on a noncommutative…
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schr\"odinger cat…
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…
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…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
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…
We show that the de Broglie-Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we…
This paper presents a thorough analysis of 1-dimensional Schroedinger operators whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. We allow both coupling constants to be complex. Using natural…
We use a recently developed formalism which generalizes the Weinberg's compositeness condition to partial waves higher than s-wave in order to determine the probability of having a $K \pi$ component in the $K^*$ wave function. A fit is made…
Multivariate quasi-projection operators $Q_j(f,\varphi, \widetilde{\varphi})$, associated with a function $\varphi$ and a distribution/function $\widetilde{\varphi}$, are considered. The function $\varphi$ is supposed to satisfy the…