The static and dynamic properties of the isotropic XY-model (s = 1/2) on the inhomogeneous periodic chain, composed of N segments with n different exchange interactions and magnetic moments, in a transverse field h are obtained exactly at arbitrary temperatures. The properties are determined by introducing the generalized Jordan-Wigner transformation and by reducing the problem to a diagonaliza...

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 in the frequency domain allows the determination of near-field diffraction, leading to the well known Fresnel diffraction when small angles are considered an...

We investigate in the equal-time formalism the derivation and truncation of infinite hierarchies of equations of motion for the energy moments of the covariant Wigner function. From these hierarchies we then extract kinetic equations for the physical distribution functions which are related to loworder energy moments, and show how to determine the higher order moments in terms of these lowest o...

The rigorous quantum mechanical definition of a resonance requires determining the pole position in the second Riemann sheet of the analytically continued partial wave scattering amplitude in the complex Mandelstam s variable plane. For meson resonances we investigate the alternative Breit-Wigner (BW) definition within the large NC expansion. By assuming that the pole position is O(N C) and exp...

Resonances in particle transmission through a 1D finite lattice are studied the presence of number impurities. Although this is one-dimensional system that classically integrable and has no chaos, studying statistical properties spectrum such as level spacing distribution spectral rigidity shows same statistics one obtained for chaotic systems. Using dimensionless parameter reflects degree stat...

A phase space description of Schrödinger dynamics is provided in terms of a quantum kinetic formalism relying on the introduction of an appropriate extension of the well-known Wigner transform, also accounting for time delocalizations. This “space-time Wigner distribution,” built up in the framework of two-time correlation functions, is shown to be governed by a non-Markovian, integro-different...

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index μ = 1/2 and the characteristic energy scale α is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential ...

The Wigner distribution (WD) can be decomposed into a linear combination of elementary WDs. Slow-oscillatory elementary WDs and fast-oscillatory elementary WDs mainly contribute to auto-terms and cross-terms, respectively. Using a weight function to keep slow-oscillatory elementary WDs and attenuate fast-oscillatory elementary WDs, one can balance auto-term resolution and cross-term suppression...

Zusammenfassung As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation that is, on the one hand, the formation of a second masterequation for the development of parameters, and, on the other hand, the use of the Wigner-distribution to describe the developmen...

Phase spaces are different ways to represent signals. Owing to their properties, they are often used for signal compression and recognition with high discrimination abilities. We present several recently introduced Wigner-related sets of representations that have improved signal processing performance, and we introduce an optical implementation. This study deals with the generalized Wigner spac...