Few-electron systems confined in quasi-one-dimensional quantum dots are studied by the configuration interaction approach. We consider the parity symmetry of states forming Wigner molecules in large quantum dots and find that for the spin-polarized Wigner molecules it strictly depends on the number of electrons. We investigate the spatial spin ordering in the inner coordinates of the quantum sy...

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a ⋆-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability ...

We present a Wigner signed particles analysis of the lensegoverned electron state dynamics based on the quantitative theory of coherence reformulated in phase space terms. Electrostatic lenses are used for manipulating electron evolution and are therefore attractive for applications in novel engineering disciplines like entangletronics. The signed particle model of Wigner evolution enables phys...

The Wigner formalism provides a convenient formulation of quantum mechanics in the phase space. Deterministic solutions of the Wigner equation are especially needed for problems where phase space quantities vary over several orders of magnitude and thus can not be resolved by the existing stochastic approaches. However, finite difference schemes have been problematic due to the discretization o...

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have propo...

Starting from a general relativistic kinetic equation, a self-consistent mean-field equation for fermions is derived within a covariant density matrix approach of QED plasmas in strong external fields. A Schrödinger picture formulation on space-like hyperplanes is applied. The evolution of the distribution function is described by the one-particle gauge-invariant 4×4 Wigner matrix, which is dec...

We prove that for [ui,j ] n i,j=1 the eigenvectors matrix of a Wigner matrix, under some moments conditions, the bivariate random process BB@ X 1≤i≤ns, 1≤j≤nt (|ui,j | − 1/n) CCA (s,t)∈[0,1]2 converges in distribution to a bivariate Brownian bridge. This result has already been proved for GOE and GUE matrices. It is conjectured here that the necessary and sufficient condition, for the result to...

Utilizing the Shift-Invariant Wavelet Packet Decomposition (SIWPD), various useful properties relevant to time-frequency analysis, including high energy concentration and suppressed interference terms, can be achieved simultaneously in the Wigner domain. A prescribed signal is expanded on its best basis and transformed into the Wigner domain. Subsequently, the interference terms are eliminated ...

We study the statistical mechanics of counterion Wigner crystals associated with hexagonal bundles of chiral biopolymers. We show that, due to spontaneous chiral symmetry breaking induced by frustration, these Wigner crystals would be chiral even if the biopolymers themselves were not chiral. Using a duality transformation of the model onto a "spin-charge" Hamiltonian, we show that melting of t...

A method for time-frequency signal analysis is presented. Theproposed method belongs to the general class of smoothed pseudo Wignerdistributions. It is derived from the analysis of the Wigner distributiondefined in the frequency domain. This method provides some substantialadvantages over the Wigner distribution. The well-known cross termeffects are reduced or completely rem...