Related papers: The Wigner distribution and 2D classical maps
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…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
We investigate the quark Wigner distribution in a frame-independent, three-dimensional position space within the framework of the dressed quark model. It is observed that the distributions are concentrated near the center of the target and…
Wigner distribution function has much importance in quantum statistical mechanics. It finds applications in various disciplines of physics including condense matter, quantum optics, to name but a few. Wigner distribution function is…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution…
The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple…
This note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is based on the scarceness of long edges in the graph and weak…
We propose an Euclidean geometric representation for the classical detection theory. The proposed representation is so generic that can be employed to almost all communication problems. The hypotheses and observations are mapped into R^N in…
Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as…
We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical orbit of a Hamiltonian system…
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example,…
We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the…
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…
The usefulness of time-frequency analysis methods in the study of quasicrystals was pointed out in a previous paper, where we proved that a tempered distribution $\mu$ on ${\mathbb R}^d$ whose Wigner transform is a measure supported on the…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators). However, in 1932, Wigner formulated quantum mechanics in terms of a distribution function…
The nearest-neighbor mass-spacing distribution of the meson and baryon spectrum (up to 2.5 GeV) is described by the Wigner surmise corresponding to the statistics of the Gaussian orthogonal ensemble of random matrix theory. This can be…
The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its…