First-order Properties Research Articles

Photon scattering from a strongly driven multi-atom system: second-order correlations and squeezing

Photon scattering from a strongly driven many-particle system is investigated. The second-order correlation function for light emitted from a strongly and near-resonantly driven dilute cloud of atoms is discussed. It is shown that photon scattering from strongly driven multi-atom systems exhibits bunching together with super-Poissonian or sub-Poissonian statistics. Next, squeezing in the resonance fluorescence emitted by a regular structure of atoms is discussed. In a suitable modified environment, squeezing even occurs for a resonant driving field, in contrast to the regular vacuum case. OCIS codes: 270.0270, 270.6620, 270.6570. doi: 10.3788/COL201210.S22701. How to characterize light is a basic but ubiquitous problem in many branches of physics. In quantum physics, correlation functions are widely used in discussing the foundations of the underlying theory. As one of the most important model system, Young’s double-slit experiment, despite its simplicity, exhibits the first-order coherence properties of light and allows to explore fundamental questions such as complementarity and uncertainty relations [1] . The remarkable progress of trapping atoms makes it possible to investigate experimentally the interference of the fluorescence light from two driven atoms which play the role of the slits in Young’s experiment [2] . In this experiment, the two slits were replaced by two 198 Hg + ions in a linear trap and the interference pattern in the light scattered from the two ions was observed. However, it was shown that, in the strong-field limit, the interference vanished at strong driving [3−10] . This restricts potential applications, e.g., coherent backscattering from disordered structures of atoms [11] , the generation of squeezed coherent light by scattering light off of a regular structure [12] , the lithography [13,14] , or precision measurements and optical information processing. The interference vanishing at strong driving can be understood from the two-particle collective dressed states. In the strong-field limit, the two-particle collective dressed states are uniformly populated, i.e., the probabilities of the symmetric transitions and of the antisymmetric transitions are the same, so that the fringes with bright center and those with dark center cancel with each other. Some of us presented a scheme to recover firstorder interference with almost full visibility in strong fields by tailoring the surrounding electromagnetic bath with a suitable frequency dependence [15] , e.g., with the help of cavities. Based on this idea, we have proposed a scheme to generate squeezing in strong driving field [16] . However, it is not possible to extract the quantum properties from the first-order correlation functions. This motivated the study of second-order correlations, initiated by the intensity-correlation experiments conducted by Hanbury-Brown et al. [17] . Subsequently, second-order correlation measurements have found ap

Face Distortion Aftereffects Evoked by Featureless First-Order Stimulus Configurations

After prolonged exposure to a distorted face with expanded or contracted inner features, a subsequently presented normal face appears distorted toward the opposite direction. This phenomenon, termed as face distortion aftereffect (FDAE), is thought to occur as a result of changes in the mechanisms involved in higher order visual processing. However, the extent to which FDAE is mediated by face-specific configural processing is less known. In the present study, we investigated whether similar aftereffects can be induced by stimuli lacking all the typical characteristics of a human face except for its first-order configural properties. We found a significant FDAE after adaptation to a stimulus consisting of three white dots arranged in a triangular fashion and placed in a gray oval. FDAEs occurred also when the adapting and test stimuli differed in size or when the contrast polarity of the adaptor image was changed. However, the inversion of the adapting image as well as the reduction of its contrast abolished the aftereffect entirely. Taken together, our results suggest that higher-level visual areas, which are involved in the processing of facial configurations, mediate the FDAE. Further, while adaptation seems to be largely invariant to contrast polarity, it appears sensitive to orientation and to lower level manipulations that affect the saliency of the inner features.

In situ variability of mass‐specific beam attenuation and backscattering of marine particles with respect to particle size, density, and composition

This study analyzes relationships between concentration of suspended particles represented by dry mass, [SPM], or area, [AC], and optical properties including particulate beam attenuation (cp), side scattering (bs), and backscattering (bbp), obtained from an intensive sampling program in coastal and offshore waters around Europe and French Guyana. First‐order optical properties are driven by particle concentration with best predictions of [SPM] by bbp and bs, and of [AC] by cp. Second‐order variability is investigated with respect to particle size, apparent density (dry weight‐to‐wet‐volume ratio), and composition. Overall, the mass‐specific particulate backscattering coefficient, bmbp ( = bbp : [SPM]), is relatively well constrained, with variability of a factor of 3–4. This coefficient is well correlated with particle composition, with inorganic particles having values about three times greater (bmbp = 0.012 m2 g−1) than organic particles (bmbp = 0.005 m2 g−1). The mass‐specific particulate attenuation coefficient, cmp ( = cp : [SPM]), on the other hand, varies over one order of magnitude and is strongly driven (77% of the variability explained) by particle apparent density. In this data set particle size does not affect cmp and affects bmbp only weakly in clear (case 1) waters, despite size variations over one order of magnitude. A significant fraction (40–60%) of the variability in bmbp remains unexplained. Possible causes are the limitation of the measured size distributions to the 2–302‐µm range and effects of particle shape and internal structure that affect bbp more than cp and were not accounted for.

Direct perturbation theory in terms of energy derivatives: Scalar-relativistic treatment up to sixth order

A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spin-free Dirac-Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavy-element compounds.

Randomizing world trade. I. A binary network analysis

The international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary or weighted, directed or undirected, aggregated or disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.

Rotation Invariance for Spatial Dispersion Property of the Elastic Constants

In this paper, invariance under rotation for the first-order and second-order spatial dispersion properties of the elastic constants was researched based on group theory. Softwares for calculating and judging invariance under arbitrary rotation of various order spatial dispersion tensors of the elastic constants were programmed by means of Mat lab. With the help of the softwares which we programmed, the general forms of the first-order and second-order spatial dispersion tensors of the elastic constants which belong to the group SO (2) were got, and it is judged that the above tensors of crystals or quasicrystals which have some degree axis of rotation had invariance under arbitrary rotation about the corresponding axes of rotation. The results were of importance to theoretical and experimental research for higher order spatial dispersion effects of the elastic constants.

On a sequence of random distance graphs subject to the zero-one law

It is known that an Erdos-Renyi random graph obeys a zero-one law for first-order properties. The study of these laws started in 1969 with the work of Yu.V. Glebskii, D.I. Kogan, M.I. Liogon'kii, and V.A. Talanov. We proved in our previous works that a random distance graph does not obey the zero-one law. In this paper a sequence of random distance graphs obeying the zero-one law is obtained.

Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian

We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of properties is taken into account by considering the full derivative of the two-component Hamiltonian matrix with respect to the external perturbation. The applicability of the analytic-gradient scheme presented here is demonstrated in benchmark calculations. SFX2c-1e results for the dipole moments and electric-field gradients of the hydrogen halides are compared with those obtained from nonrelativistic, SF high-order Douglas-Kroll-Hess, and SF Dirac-Coulomb calculations. It is shown that the use of untransformed two-electron interactions introduces rather small errors for these properties. As a first application of the analytic geometrical gradient, we report the equilibrium geometry of methylcopper (CuCH(3)) determined at various levels of theory.

Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian

We report an analytical scheme for the calculation of first-order electrical properties using the spin-free Dirac-Coulomb (SFDC) Hamiltonian, thereby exploiting the well-developed density-matrix formulations in nonrelativistic coupled-cluster (CC) derivative theory. Orbital relaxation effects are fully accounted for by including the relaxation of the correlated orbitals with respect to orbitals of all types, viz., frozen-core, occupied, virtual, and negative energy state orbitals. To demonstrate the applicability of the presented scheme, we report benchmark calculations for first-order electrical properties of the hydrogen halides, HX with X = F, Cl, Br, I, At, and a first application to the iodo(fluoro)methanes, CH(n)F(3 - n)I, n = 0-3. The results obtained from the SFDC calculations are compared to those from nonrelativistic calculations, those obtained via leading-order direct perturbation theory as well as those from full Dirac-Coulomb calculations. It is shown that the full inclusion of spin-free (SF) relativistic effects is necessary to obtain accurate first-order electrical properties in the presence of fifth-row elements. The SFDC scheme is also recommended for applications to systems containing lighter elements because it introduces no extra cost in the rate-determining steps of a CC calculation in comparison to the nonrelativistic case. On the other hand, spin-orbit contributions are generally small for first-order electrical properties of closed-shell molecules and may be handled efficiently by means of perturbation theory.

Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory

In this work, we present relativistic corrections to first-order electrical properties obtained using fourth-order direct perturbation theory (DPT4) at the Hartree-Fock level. The considered properties, i.e., dipole moments and electrical-field gradients, have been calculated using numerical differentiation techniques based on a recently reported DPT4 code for energies [S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)]. For the hydrogen halides HX, X=F, Cl, Br, I, and At, we study the convergence of the scalar-relativistic contributions by comparing the computed DPT corrections to results from spin-free Dirac-Hartree-Fock calculations. Furthermore, since in the DPT series spin-orbit contributions first appear at fourth order, we investigate their magnitude and judge the performance of the DPT4 treatment by means of Dirac-Hartree-Fock benchmark calculations. Finally, motivated by experimental investigations of the molecules CH(2)FBr, CHF(2)Br, and CH(2)FI, we present theoretical results for their halogen quadrupole-coupling tensors and give recommendations concerning the importance of higher-order scalar-relativistic and spin-orbit corrections.

Adjusted intraclass correlation coefficients for binary data: methods and estimates from a cluster-randomized trial in primary care

Accurate estimates of the intraclass correlation coefficient (ICC) are important for calculating appropriate sample sizes for cluster-randomized trials. The ICC and hence the sample size may be reduced through adjustment for baseline covariates. A method exists for calculating adjusted ICCs for binary outcomes based on the logit link, used to calculate odds ratios. Recent interest in presenting relative risks rather than odds ratios indicates that a method based on the log link is needed. To determine and evaluate a method for calculating adjusted ICCs based on the log link, and to provide and compare unadjusted and adjusted ICCs from a cluster-randomized trial in primary care based on the logit and log link. Two methods are proposed for calculating adjusted ICCs for the log link based on a first-order Taylor series expansion and properties of the lognormal distribution. The methods are evaluated by simulation. Unadjusted and adjusted ICCs are calculated for binary outcomes from the Point of Care Testing (PoCT) Trial using the logit and log link. The methods for calculating adjusted ICCs for the log link produced similar results unless the between cluster variance was large. Unadjusted ICCs for the PoCT Trial ranged from 0.001 to 0.048. The impact of adjustment on the ICC varied between outcomes and link functions, ranging from a 59% reduction to an 89% increase. The true ICC was unknown for the simulation study. Adjustment was made for age and gender only for the PoCT Trial. The method for calculating adjusted ICCs for binary outcomes depends on the link function. For the log link, the method based on the lognormal distribution is recommended. This method will be useful for cluster-randomized trials where the relative risk, rather than the odds ratio, is the effect measure of interest.

Local CC2 response method for triplet states based on Laplace transform: Excitation energies and first-order properties

A new multistate local CC2 response method for calculating excitation energies and first-order properties of excited triplet states in extended molecular systems is presented. The Laplace transform technique is employed to partition the left/right local CC2 eigenvalue problems as well as the linear equations determining the Lagrange multipliers needed for the properties. The doubles part in the equations can then be inverted on-the-fly and only effective equations for the singles part must be solved iteratively. The local approximation presented here is adaptive and state-specific. The density-fitting method is utilized to approximate the electron-repulsion integrals. The accuracy of the new method is tested by comparison to canonical reference values for a set of 12 test molecules and 62 excited triplet states. As an illustrative application example, the lowest four triplet states of 3-(5-(5-(4-(bis(4-(hexyloxy)phenyl)amino)phenyl)thiophene-2-yl)thiophene-2-yl)-2-cyanoacrylic acid, an organic sensitizer for solar-cell applications, are computed in the present work. No triplet charge-transfer states are detected among these states. This situation contrasts with the singlet states of this molecule, where the lowest singlet state has been recently found to correspond to an excited state with a pronounced charge-transfer character having a large transition strength.

The effect of local approximations on first-order properties from expectation-value coupled cluster theory

The accuracy of local approximations has been studied for expectation-value coupled cluster theory restricted to single and double excitations (XCCSD), applied to first-order one-electron molecular properties, such as dipole and quadrupole moments. The analysis has been performed separately for each component of the XCCSD expression, which allows to gauge the sensitivity of various parts of the formula to the localization conditions. The varying impact of local approximations is explained by examining the most important terms in the Moller-Plesset expansion of the first-order XCCSD property formula. It has been found that the contribution from the singly excited cluster operator plays a dominant role in the correlation part of the property, and that the common local settings, which consist in including only strong orbital pairs in the CCSD residual equations, lead to significant errors in the local multipole moments. Fortunately, the Moller-Plesset analysis of the XCCSD method allows to formulate a modified set of local approximations, which is better suited for a description of first-order properties. The new options involve the inclusion of close pairs into the CCSD residual equations and the extension of the strong-pair domains, which considerably improves the agreement of the singles-dependent part of the property with the nonlocal reference value. Additionally, for an accurate description of the part of the XCCSD expression containing the doubly excited cluster operator, it is necessary to include close and weak pairs from local MP2 theory. The mean absolute percent error of the correlation part of the dipole moment for the test set of 31 molecules in the cc-pVDZ basis amounts to 16% with the standard local settings, but can be reduced to only 5%, if the new set of local approximations is utilized instead. The existence of local approximations that are appropriate for local XCCSD opens a possibility to calculate first-order properties for large molecules on the coupled cluster level, without a need to solve an additional expensive set of equations for the zeroth-order Lagrangian multipliers from response coupled cluster theory.

Symplecticity and relationships among the fundamental properties in linear optics

Because of symplecticity the four fundamental first-order optical properties of an optical system are not independent. Relationships among them reduce the number of degrees of freedom of a system’s transference from 16 to 10. There are many such relationships, they are not easy to remember, they take many forms and they are often needed in derivations. The purpose of this paper is to provide in one place a comprehensive collection of those that have proved useful in linear optics generally and in the context of the eye particularly. The paper also offers aids to memorizing some of the results, derives most of them and along the way introducesthe basic notions underlying symplecticity. The relationship to another important class of matrices, the Hamiltonian matrices, is discussed together with their potential role in statistical analysis of the eye. Augmented symplectic matrices are also defined and their relationship to augmented Hamiltonian matrices described. An appendix gives numerical examples of symplectic and Hamiltonian matrices and shows how they may be recognized and constructed. (S Afr Optom 2010 69(1) 3-13)

Epitaxy surface effect on the first-order phase transition properties in a ferroelectric thin film

By modifying the interchange interactions and the transverse fields on the epitaxy surface layer, this paper studies the phase transition properties of an n-layer ferroelectric thin film by the Fermi-type Green's function technique based on the transverse Ising model with a four-spin interaction. The special attention is given to the effect of the epitaxy surface layer on the first-order phase transition properties in the parameter space constructed by the ratios of the bulk transverse field and the bulk four-spin interaction to the bulk two-spin interaction with the framework of the higher-order decoupling approximation to the Fermi-type Green's function. The results show that the first-order phase transition properties will be changed significantly due to the modification of interchange interaction and transverse field parameters on the epitaxy surface layer. The dependence of the first-order phase transition properties on the thickness of ferroelectric thin films is also discussed.

DOES M31 RESULT FROM AN ANCIENT MAJOR MERGER?

The numerous streams in the M31 halo are currently assumed to be due to multiple minor mergers. Here we use the GADGET2 simulation code to test whether M31 could have experienced a major merger in its past history. It results that a 3+/-0.5:1 gaseous rich merger with r(per)=25+/-5 kpc and a polar orbit can explain many properties of M31 and of its halo. The interaction and the fusion may have begun 8.75+/-0.35 Gyr and 5.5 +/-0.5 Gyr ago, respectively. With an almost quiescent star formation history before the fusion we retrieve fractions of bulge, thin and thick disks as well as relative fractions of intermediate age and old stars in both the thick disk and the Giant Stream. The Giant Stream is caused by returning stars from a tidal tail previously stripped from the satellite prior to the fusion. These returning stars are trapped into elliptical orbits or loops for almost a Hubble time period. Large loops are also predicted and they scale rather well with the recently discovered features in the M31 outskirts. We demonstrate that a single merger could explain first-order (intensity and size), morphological and kinematical properties of the disk, thick disk, bulge and streams in the halo of M31, as well as the distribution of stellar ages, and perhaps metallicities. It challenges scenarios assuming one minor merger per feature in the disk (10 kpc ring) or at the outskirts (numerous streams & thick disk). Further constraints will help to properly evaluate the impact of such a major event to the Local Group.

Bare nominals and incorporating verbs in Spanish and Catalan

This paper presents an analysis of bare nominals unmarked for number (BNs) occurring in object position in Spanish and Catalan, on which the BN is a syntactic complement to the verb, but not a semantic argument. After describing the properties that distinguish BNs from other indefinite expressions (bare plurals, indefinite singulars preceded by un ‘a’, and bare mass terms), we argue that these BNs occur in a monadic syntactic configuration in the sense of Hale & Keyser (1998), that they denote first-order properties, and that they are combined with the verb via a modified version of Dayal's (2003) semantics for pseudo-incorporation. Specifically, the proposal consists of a lexical rule that generates the class of verbs that productively accept BN objects, plus a composition rule that treats the BN as modifier of the verb. We point out the advantages of this analysis over three other well-known semantic analyses for combining verbs with property-type nominals. Finally, we show how the analysis can be naturally extended to existential sentences, which combine with BNs although, prima facie, they do not appear to meet the lexical conditions for doing so.

One‐Stop Stereology: the estimation of 3D parameters using Isotropic Rulers

The stereological estimation of second-order descriptors of spatial architecture appears to be inherently more time-consuming and labour-intensive than the estimation of first-order quantities (total quantities or ratios). Therefore, far fewer researchers tend to make use of second-order approaches in their stereological research projects. In this paper, we use a tutorial approach to illustrate how a desire for practical simplicity has provided us with a data collection method that can be used to simultaneously estimate both first-order and second-order properties of the microstructure of a defined anatomical feature of an organ. The approach does not rely on new results from theory, but nevertheless allows either isotropic uniform random or vertical uniform random sections to be used to make estimates of a comprehensive list of 10 microstructural parameters using relationships that are well known in the literature. The probe used in all cases is an isotropically distributed Ruler and the data collection protocol is easy to learn and apply. We illustrate the method on brain tissue but emphasize that the approach can also be applied to non-biological material.

GEL METHODS FOR NONSMOOTH MOMENT INDICATORS

This paper considers the first-order large sample properties of the generalized empirical likelihood (GEL) class of estimators for models specified by nonsmooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient generalized method of moments (GMM) estimator that may suffer from substantial biases in finite samples. These include empirical likelihood (EL), exponential tilting (ET), and the continuous updating estimator (CUE). This paper also establishes the validity of tests suggested in the smooth moment indicators case for overidentifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix that may be problematic for the sample sizes typically encountered in practice.

Analytic Calculation of First-order Molecular Properties at the Explicitly-correlated Second-order Møller-Plesset Level

Abstract Formulae are derived and implemented for the analytic calculation of first-order molecular properties at the level of explicitly-correlated second-order Møller-Plesset perturbation theory. In this theory, which is denoted as MP2-F12 theory, Slater-type geminals are used to expand the first-order wave function. A second-order perturbation theory correction for single excitations into a complementary auxliary basis set is also included. At the MP2-F12 level, it seems sufficient to restrict the analytic calculation of energy derivatives to the level of standard approximation A of MP2-F12 theory and to assume the extended Brillouin condition to hold. Smooth and rapid convergence towards the basis-set limit is observed for the dipole moments of a selection of small closed- and open-shell molecules when calculated at the RI-MP2-F12/2A*[T+V] + CABS singles level in augmented correlation-consistent polarized valence double-, triple-, and quadruple-zeta basis sets that have been optimized especially for use in MP2-F12 theory.