Related papers: Detecting quasicrystals with quadratic time-freque…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…
We investigate the $\tau$-quantizations and Cohen's class distributions of a suitable class of trace-class operators, called Feichtinger's operators, and show that it is a convenient substitute for the class of Schwartz operators. Many…
Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin $-1/2$ state of quark…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
Extraordinary new materials named quasicrystals and characterized by noncrystallographic rotational symmetry and quasiperiodic translational properties have attracted scrutiny. Study of quasicrystals may shed light on the most basic notions…
In this thesis we present a direct scheme for measuring quasidistribution functions of light. This scheme, based on photon counting, is derived from a simple relation linking the Wigner function with photon statistics. We develop a full…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
Wigner crystal, as the most fundamental exemplification where the many-body interaction forges the electrons into a solid, experiences an intriguing quantum melting where diverse intermediate phases are predicted to emerge near the quantum…
The analysis of Fourier-transformed scanning-tunneling-microscopy (STM) images with subatomic resolution is a common tool for studying properties of quasiparticle excitations in strongly correlated materials. While Fourier amplitudes are…
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…
Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the…
A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a…
Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration…
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…