Wigner functions are functions on classical phase space, which are in one-to-one correspondence to square integrable functions on configuration space. For molecular quantum systems, classical transport of Wigner functions provides the basis of asymptotic approximation methods in the high energy regime. The article addresses the sampling of Wigner functions by Monte Carlo techniques. The approxi...

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of t...

This article presents a new method facilitating interference reduction in the Wigner-Ville distribution, which is used for nonstationary signal analysis, for example in machine condition monitoring. The algorithm is based on multiple Smoothed Pseudo Wigner-Ville distributions: differently smoothed time-frequency planes are compared and, for every point, a cross-term free value is calculated on ...

We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the spa...

We report diffusion quantum Monte Carlo calculations of three-dimensional Wigner crystals in the density range rs5100–150. We have tested different types of orbital for use in the approximate wave functions but none improve upon the simple Gaussian form. The Gaussian exponents are optimized by directly minimizing the diffusion quantum Monte Carlo energy. We have carefully investigated and sough...

We consider N ×N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e. We prove that the eigenvalue statistics in the bulk is given by Dyson sine kernel provided that U ∈ C(R) with at most polynomially growing derivatives and ν(x) ≤ C e for x large. The proof is based upon an approximate time reversal of the Dyson Brownian mot...

A discrete-time, discrete-frequency Wigner distribution is derived using a group-theoretic approach. It is based upon a study of the Heisenberg group generated by the integers mod N , which represents the group of discrete-time and discrete-frequency shifts. The resulting Wigner distribution satis es several desired properties. An example demonstrates that it is a full-band time-frequency repre...

In this study a time-frequency method based on Wigner-Ville Distribution (WVD) is used for detection and parameter estimation of Frequency Modulated Continuous Wave (FM-CW) Radar Signal. The proposed method uses the Pseudo-Wigner-Ville Distribution (PWVD) as a time-frequency detection technique and Radon Transform to identify the parameter of the modulation. The Wigner-Ville Radon Transform (WV...

The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function which reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the...

– The Wigner equation taking into account both the non-local potential operator and a scattering operator represents a suitable physical model for carrier transport in nano structures. In this paper a new Monte Carlo method is proposed for the solution of the stationary Wigner equation. Scattering can be included at the level of the semi-classical Boltzmann scattering operator, whereas coherent...