Quantum erasure within the Optical Stern-Gerlach Model

In the optical Stern-Gerlach effect the two branches in which the incoming atomic packet splits up can display interference pattern outside the cavity when a field measurement is made which erases the which-way information on the quantum paths the system can follow. On the contrary, the mere possibility to acquire this information causes a decoherence effect which cancels out the interference pattern. A phase space analysis is also carried out to investigate on the negativity of the Wigner function and on the connection between its covariance matrix and the distinguishability of the quantum paths.Comment: 7 pages, 3 figure

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media

We derive exact strong-contrast expansions for the effective dielectric tensor \epeff of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for \epeff to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing $n$-point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the {\it coarseness} of the composite, i.e., local volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure

Asymmetry Function of Interstellar Scintillations of Pulsars

A new method for separating intensity variations of a source's radio emission having various physical natures is proposed. The method is based on a joint analysis of the structure function of the intensity variations and the asymmetry function, which is a generalization of the asymmetry coefficient and characterizes the asymmetry of the distribution function of the intensity fluctuations on various scales for the inhomogeneities in the diffractive scintillation pattern. Relationships for the asymmetry function in the cases of a logarithmic normal distribution of the intensity fluctuations and a normal distribution of the field fluctuations are derived. Theoretical relationships and observational data on interstellar scintillations of pulsars (refractive, diffractive, and weak scintillations) are compared. Pulsar scintillations match the behavior expected for a normal distribution of the field fluctuations (diffractive scintillation) or logarithmic normal distribution of the intensity fluctuations (refractive and weak scintillation). Analysis of the asymmetry function is a good test for distinguishing scintillations against the background of variations that have different origins

Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons

The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner- Liouville's type equation has been derived. The numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed. For electrons in disordered systems of scatterers the numerical results have been obtained for series of the average values of the quantum operators including position and momentum dispersions, average energy, energy distribution function as well as for the frequency dependencies of tensor of electron conductivity and permittivity according to quantum Kubo formula. Zero or very small value of static conductivity have been considered as the manifestation of Anderson localization of electrons in 1D case. Independent evidence of Anderson localization comes from the behaviour of the calculated time dependence of position dispersion.Comment: 8 pages, 10 figure

Exact positivity of the Wigner and P-functions of a Markovian open system

We discuss the case of a Markovian master equation for an open system, as it is frequently found from environmental decoherence. We prove two theorems for the evolution of the quantum state. The first one states that for a generic initial state the corresponding Wigner function becomes strictly positive after a finite time has elapsed. The second one states that also the P-function becomes exactly positive after a decoherence time of the same order. Therefore the density matrix becomes exactly decomposable into a mixture of Gaussian pointer states.Comment: 11 pages, references added, typo corrected, to appear in J. Phys.

Photon Distribution Function for Long-Distance Propagation of Partially Coherent Beams through the Turbulent Atmosphere

The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave correlations are described in terms of photon trajectories that depend on fluctuations of the refractive index. It is shown that both linear and quadratic disturbances produce sizable effects for long-distance propagation. The quadratic terms are shown to suppress the correlation of waves with different wave vectors. We examine the intensity fluctuations of partially coherent beams (beams whose initial spatial coherence is partially destroyed). Our calculations show that it is possible to significantly reduce the intensity fluctuations by using a partially coherent beam. The physical mechanism responsible for this pronounced reduction is similar to that of the Hanbury-Braun, Twiss effect.Comment: 28 pages, 4 figure

Scintillation Reduction for Laser Beams Propagating Through Turbulent Atmosphere

We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. These studies were performed for different dimensions of the detector, distances of propagation, and strengths of the atmospheric turbulence. Methods for significantly reducing the scintillation index are described. These methods utilize averaging of the signal at the detector over a set of partially coherent beams (PCBs). It is demonstrated that the most effective approach is using a set of PCBs with definite initial directions of propagation relative to the z-axis. This approach results in a significant compensation of the beam wandering which in many cases is the main contributor to the SI. A novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the effective suppression of the SI does not require high-frequency modulators. This result is important for achieving gigabit data-rates in long-distance laser communication through turbulent atmospheres.Comment: 35 pages, 29 figure

Peculiarities of the Weyl - Wigner - Moyal formalism for scalar charged particles

A description of scalar charged particles, based on the Feshbach-Villars formalism, is proposed. Particles are described by an object that is a Wigner function in usual coordinates and momenta and a density matrix in the charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach explicitly contains a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of the coordinate operator. The evolution equation for the Wigner function of a single-charge state in the classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.Comment: 16 pages, 2 figure

On the Wigner function of the relativistic finite-difference oscillator in an external field

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner quasi-distribution function for the stationary states as well as of states of thermodynamical equilibrium are obtained and their correct limits are shown.Comment: 12 pages, 6 figures, IOP styled LaTeX, to be published in Journal of Physics

Bottleneck effects in turbulence: Scaling phenomena in r- versus p-space

We (analytically) calculate the energy spectrum corresponding to various experimental and numerical turbulence data analyzed by Benzi et al.. We find two bottleneck phenomena: While the local scaling exponent $\zeta_r(r)$ of the structure function decreases monotonically, the local scaling exponent $\zeta_p(p)$ of the corresponding spectrum has a minimum of $\zeta_p(p_{min})\approx 0.45$ at $p_{min}\approx (10 \eta)^{-1}$ and a maximum of $\zeta_p(p_{max})\approx 0.77$ at $p_{max}\approx 8 L^{-1}$. A physical argument starting from the constant energy flux in p--space reveals the general mechanism underlying the energy pileups at both ends of the p--space scaling range. In the case studied here, they are induced by viscous dissipation and the reduced spectral strength on the scale of the system size, respectively.Comment: 9 pages, 3figures on reques