Coherency matrix description for statistical linear regression of Stokes parameters in rough small-particle scattering

A statistical analysis of the Stokes parameters in light scattering by randomly rough small particles shows a linear regression law between the squares of the first two components I_s and Q_s of the Stokes vector. While the coefficients of this linear regression contain physical characteristics of the particles, they cannot be directly interpreted in terms of the degree of polarization of the scattered field. We propose an interpretation of this relationship between the Stokes parameters on the basis of the general coherence-density matrix formalism. The link between the statistical regression results and the polarization properties of the stochastic scattered components of the field is established through the coherency matrix elements.     

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers.     

On normalization of scattering matrices of polarized radiation

The condition of normalization of scattering matrix is derived when the polarized radiation is described by the Stokes parameters I, Q, U, V. The normalization of the matrix is based on energy conservation. It has a probabilistic meaning also. When the scattering particle is nonspherical, scattered radiation may depend not only on the angle between incident and scattered radiation but on orientation of the scattering plane also. In these cases, the known change of the Stokes parameters Q, U of the incident radiation with respect to various scattering planes influences the normalization. The derived normalization includes all elements of the first line of scattering matrix and the characteristics of polarization of the incident radiation. Dependence on this polarization is appeared because the polarization influences intensities of scattered radiation and, therefore, is included in energy conservation. The routine normalization includes the first element of the scattering matrix only. These two normalizations determine the different normalizing constants of the scattering matrix. The simple computational example of scattering by the particle that has the shape of a finite cylinder is considered. This example shows that the values of normalizing constants of the routine normalization may considerably differ from the ones of the obtained normalization. The results of the study may be useful in various investigations of radiation scattering, especially in the cases when the scattering particles are nonspherical.     

Charge and orbital ordering in Na0.5CoO2

The ground state of Na_0.5CoO₂ has been calculated using the full potential local orbital method and local density approximation plus Hubbard U (); the results demonstrate that charge and orbital ordering evidently exist in the present system in association with the antiferromagnetic state. Notable structural features observed between 300 and 30 K have been carefully examined using in situ TEM investigations, a superstructure with a wave vector of Q1=a^∗/2, becoming commonly visible below , can be interpreted as the charge/orbital ordering on the Co1 and Co2 sites. Moreover, we have also observed another notable superstructure with Q2=a^∗/4 below the phase transition of , which suggests a more complicated orbital ordered state existing at lower temperatures.     

Applications of the master equation of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time-dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a coherent laser field and damped by a finite-bandwidth squeezed vacuum. The master equation has the standard form known from the broadband squeezing approaches but with new effective squeezing parameters and and new rate coefficients. There are also new terms, proportional to β, which are essentially narrow-bandwidth modifications determined by the parameters γ_n, δ_n and the shifts δ_N and δ_M. These parameters become zero when the squeezing bandwidth tends to infinity. The effects of the detuning parameter Δ of the driving laser field frequency ω_L from the atomic resonance ω_A and the squeezing parameters and on the atomic inversion, the von Neumann entropy and the resonance fluorescence spectrum are discussed.     

Gas-phase detection of discharge-generated DSOD

We report the first spectroscopic detection of perdeuterated 1-oxadisulfane, DSOD, generated in a radio-frequency plasma of D₂S and D₂O. The chain molecule DSOD produces a perpendicular-type spectrum, with well-known spectral features encountered in previous studies of geometrically related molecules, such as compact Q-branches, which are clearly recognizable. The arrangement of the transitions shaping the Q-branches usually provides sufficient proof for a clear-cut detection of a chain molecule such as DSOD. Guided by quantum chemical calculations, we have located the band center of the -branch of DSOD in the frequency region near 466.5 GHz using the Cologne terahertz spectrometer. This -branch displays both b- and c-type spectra, quite analogous to the behavior of the corresponding -branch of HSOH. In addition, we have been able to detect an internal rotational splitting of ∼0.5 MHz for c-type transitions of the -branch, which lends independent support to our present assignment. From the measurements performed on Q-branches, we derive the following differences in rotational constants: A−(B+C)/2=93331.001(15) MHz, and (B−C)/4=172.95923(29) MHz, in excellent agreement with theoretical predictions.     

Ultraboundedness for parabolic equations in convex domains without boundary conditions

We consider the operator , where U is a convex real function defined in a convex open set O⊂R^N and lim_|x|→∞U(x)=lim_x→∂OU(x)=+∞. We prove that the associated Markov semigroup is ultrabounded with respect to the Gibbs measure .     

Energy structure of Er-2O center in GaAs:Er,O studied by high magnetic field photoluminescence measurement

We perform photoluminescence measurement of GaAs:Er,O under a pulsed magnetic field up to 60 T and succeed to obtain the magnetic field dependence of three main photoluminescence peaks. We also estimate the energy splitting of states ⁴I_15/2 and ⁴I_13/2 using the crystal field theory. Theoretically calculated energy differences between the lowest state of J= and the lowest three states of J= are in good agreement with experimentally obtained energy of three main PL peaks. We discuss the local configuration around the luminescent Er-2O center. By using parameters in the crystal field calculation, our analysis suggest that not only O²⁻ sites but also As³⁻ sites adjacent to Er³⁺ ion are displaced from their original lattice positions.     

About the Stokes decomposition theorem of waves

The Stokes decomposition theorem deals with the electrical field of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a “strong definition” of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a “weak definition”, solutions are given by elementary properties of bidimensional random variables.     

Doppler-limited spectroscopy of the AΠ1 ← XΣ system of ICl in the 0.8 μm region using a Ti:sapphire ring laser

Doppler-limited vib-rotational absorption spectra of the A ← X electronic transition of I^35/37Cl are measured in the range 11,352-13,507 cm⁻¹ using a Ti:sapphire ring laser. The P-, Q-, and R-branch lines belonging to the v ← v″ = (0-7) ← (0-7) transition in I³⁵Cl and the v ← v″ = (0-6) ← (2-6) transition in I³⁷Cl are assigned. Under Doppler-limited conditions, the P- and R-branch lines are split into doublets by the nuclear quadrupole coupling effect of the I atom. The unperturbed positions of these lines are correctly calculated, whereas splitting in the Q-branch lines was not observed. The mass-reduced Dunham expansion coefficients U_l,m of the A and X states and the spectroscopic constants , and H_v^′ of the A state are determined using a global least-squares fitting procedure.     

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

Clebsch-Gordan coefficients for the extended quantum-mechanical Poincaré group and angular correlations of decay products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum-mechanical Poincaré group . ‘Extended’ refers to the extension of the 10 parameter Lie group that is the Poincaré group by the discrete symmetries C, P, and T; ‘quantum mechanical’ refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here is applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of with positive energy to irreducible components. Of the 16 inequivalent representations of the discrete symmetries, the two standard representations with U_CU_P = ±1 are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the ? (4S) meson.