Based on the equal-time Wigner function for the Klein-Gordon field, we discuss analytically the mechanism of pair creation in a classical electromagnetic field including back-reaction. It is shown that the equations of motion for the Wigner function can be reduced to a variable-frequency oscillator. The pair-creation rate results then from a calculation analogous to barrier penetration in nonre...

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conducti...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

Micro-Doppler signatures provide unique information about properties of the target. These micro-Doppler features can be used for real time target recognition in military applications and surveillance operations. In this paper, we present Gabor-Wigner transform for extracting micro-Doppler features from the radar returns. The effectiveness of the GaborWigner transform in extracting micro-Doppler...

Assuming that the phase transition between the Wigner solid and the Laughlin liquid is first-order, we compare ground-state energies to find features of the phase diagram at fixed ν. Rather than use the Coulomb interaction, we calculate the effective interaction in a square quantum well, and fit the results to a model interaction with length parameter λ roughly proportional to the width of the ...

(Q1). = Q3, (Q2)w = -(Qi + Q2)/V/2, (Q3)D = (Q2 Q1)//2, (Q4)w = Q4. There are similar relations between the Wigner co-ordinates and our co-ordinates of Fig. 4, d. Wigner states that if the number of particles is a power of 2 and the masses are equal, there is a co-ordinate system of high symmetry in which all particles are treated equally. Unfortunately the form of the potential energy in the c...

Conditional probability distributions from exact diagonalization are used to investigate the crystalline or liquid character of the downward cusp states in parabolic quantum dots (QD’s) at high magnetic fields. These states are crystalline in character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with t...

The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein–Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein–Gordon field are derived. It is shown that they lea...

The Wigner function is a quasiprobability density over phase space (for reviews, see Lee[1], Cohen[2], or Hillery et al.[3]; a quasiprobability is generally not positive semi-definite), so in a quantum field theory setting it is not manifestly Lorentz covariant. Quasiprobabilities are conceptually interesting partly because Arthurs-Kelly type interpretations of positive definite Husimi function...

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski spacetime and then restricted to Wigner hyperplanes to get their description in the rest-frame Wigner-covariant instant form of dynamics. The canonical reduction to the Wigner-covariant Coulomb gauge is done in the rest frame. It is sh...