Related papers: Wigner transform and quasicrystals
We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $\omega$ is described by the scattering matrix $\mathcal{S}(\omega)$, encoding the probability…
We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related, and in fact in competition, with the possibility of damping the…
For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids.…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…
We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function…
Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of…
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…
The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions…
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…
Every set $\Lambda\subset R$ such that the sum of $\delta$-measures sitting at the points of $\Lambda$ is a Fourier quasicrystal, is the zero set of an exponential polynomial with imaginary frequencies.
Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
We calculate quark Wigner distributions using the light-front wave functions in a dressed quark model. In this model, a proton target is replaced by a simplified spin-1/2 state, namely a quark dressed with a gluon. We calculate the Wigner…
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…
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of…
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 develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant $\hbar$. We demonstrate to any order of…
In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and $\tau$-Wigner distributions, using metaplectic operators. However, in order for a metaplectic…