Origin Of Divergences Research Articles

Geographical variation in size of the three final stadia of Cordulegaster boltonii (Donovan, 1807) larvae in the Iberian Peninsula (Odonata: Cordulegastridae)

A two-variable analysis of male and female Cordulegaster boltonii larvae (head width and hindwing sheath length) in specimens from five Iberian populations was carried out with the objective of ascertaining whether these traits differ between populations. The results indicate that the southernmost population (Los Alcornocales, Andalusia) have larger sizes for both variables and a lower growth rate between the penultimate and final stadia. Winter water temperatures, which may cause a longer arrest of larval growth in northern populations, and possible differences in the number of larval stadia could be the origin of the size divergences.

Entanglement entropy across the lattice-continuum correspondence

This paper revisits the standard calculations of free field entanglement entropy in light of the newly developed lattice-continuum correspondence. This correspondence prescribes an explicit method to extract an approximately continuum quantum field theory out of a fully regularized lattice theory. This prescription will here be extended to subregion algebras, and it will be shown how entropies of continuum boson and fermion theories can be computed by working purely with lattice quantities. This gives a clear picture of the origin of divergences in entanglement entropy while also presenting a concise and detailed recipe for calculating this important quantity in continuum theories.

On the origin of divergences in time-dependent orbifolds

We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off.

Selected English, German, and Polish Phraseological Units about Human Communication: An Attempt of a Comparative Analysis

Undoubtedly, phraseological units constitute one of the most fascinating aspects of the language, especially with regard to their illustrative and often abstract meaning contrasted with their equivalents in other languages. Describing the same phenomena, they often emphasise distinct elements. For instance, in English one can lie through one’s teeth , however, one neither needs teeth to lie in Polish, as eyes are indispensable ( kłamać komuś w żywe oczy ), nor in German – in this case, all that is necessary is somebody’s face ( jemandem glatt ins Gesicht lügen ). In order to beat about the bush , cotton is required in Polish ( owijać w bawełnę ) and flowers in German ( etwas durch die Blumen sagen ). Nevertheless, in some cases the equivalence rate is considerably high ( lay one’s cards on the table – wyłożyć karty na stół – die Karten offen auf dem Tisch legen ). However, speaking off the cuff has hardly anything in common with its German equivalent ( aus dem hohlen Bauch heraus sprechen ), whereas the Polish equivalent ( mówić bez przygotowania ) is not even deemed a phraseological unit at all. This article is an attempt at a comparative analysis of selected English, German, and Polish phraseological expressions concerning human communication with regard to both their idiomaticity degree in accordance to typologies by Harald Burger (2010), Christiane Römer and Brigitte Matzke (2005) and the represented equivalence type, based on classifications by Hessky (1992), and Laskowski (2003). Finally, the question regarding the linguistic worldview, the origin of convergences and divergences between the aforementioned expressions, is touched upon.

Quantum chains and regularisation of quantum dynamics

We argue that the origin of ultraviolet divergences in quantum field theory (QFT) may be not in the perturbative expansion, but in the fact that, mathematically, the Heisenberg equations of motion are not properly defined. Divergences similar to those in QFT are shown to exist in seemingly simple quantum problems with parametric Hamiltonians. These divergences may be suppressed by formally replacing the system in question by a quantum chain. The latter is a dynamically regularised system specified by two postulates, imposing conditions on its response properties. The kinematical postulate specifies the linear response, the dynamical postulate extends it to nonlinear dynamics. The kinematical postulate uniquely determines the mathematical environment (quantisation with indefinite metric), hence the term. Using the Klein–Gordon, Gupta–Bleuler and Dirac fields as examples we show that the concept of quantum chain generalises seamlessly to relativistic quantum fields. Perspectives of using quantum chains as regularisation devices in QFT are discussed.

The “Sino-barbarian dichotomy” amid the political chess of China’s dynasties: In the examples of the Song, Liao, and Jin dynasties

The “Sino-barbarian dichotomy” (華夷之辨 Hua yi zhi bian) was a major theme in China’s ancient historical debates: even today, scholarly circles have produced a welter of opinions as to the merits of the “Sino-barbarian dichotomy,” and even as to the standards for differentiating between the “Chinese” (華 Hua) and the “barbarians” (夷 yi). In tracing the idea to its source, the Confucians noted correctly that the only standard for the “Sino-barbarian dichotomy” is cultural (not including race or geographical origin): this implies a veneration for “civilization” coupled with the denigration of “barbarism,” with the aim of constructing a “grand unified” order for “All Under Heaven” through ritual culture. In practicing the politico-cultural concept of “Sino-barbarian dichotomy,” dynastic rulers and the literati community frequently brought it into play on the basis of practical political considerations, and even deliberately blurred or distorted the broad and narrow connotations of the terms Chinese and barbarian. This is the origin of the many divergences in understanding and disagreements among scholarly circles regarding the “Sino-barbarian dichotomy.” We can clarify this understanding if we approach the intrinsic meaning of the “Sino-barbarian dichotomy” from a pragmatics’ perspective: political practices from the Song, Liao, and Jin dynasties amply reflect the active role played by the “Sino-barbarian dichotomy” in spurring the formation of the Chinese people.

THE ACTUAL PROBLEMS OF THE FUNCTIONING OF SOCIAL-LABOR RELATIONS IN THE REGION

In the article the features of functioning of sociallabour relations are investigational in an agrarian region, the important problems of their development that results in regional differences in quality of life of population are educed. A labour-market to the Ternopil area depends on changes in an economy, demographic and social tendencies, and also from the row of other specific factors (level of remuneration of labour, seasonal character of production, disbalance at the market of labour, labour migration, "shadow employment" and other) that became reasons of origin of disproportions in development of sociallabour relations in a region. By basic factors that predetermined the origin of sociallabour divergences (conflicts) in a region were : debt from payment of salary; non-fulfillment of conditions of the collective agreement; non-fulfillment of requirements of legislation is about labour. For today in a region the different models of relations are widespread between workers and employers, but their basic maintenance is prevailing of side of employers. In the article the issues of the day of functioning of sociallabour relations are certain in a region, namely: socially unfair salary and excessive differentiation in the acuestss of population; transformation of institute of employment; a force underemployment (of work is in the conditions of incomplete workday (of week), of vacation without maintenance of salary; existence of shadow employment; high unemployment rate; violation and ignoring of terms of collective labour agreements (of agreements) by employers, violation of labour rights and ignoring of necessities of the hired workers; total increase of mistrust to the employers, leaders of enterprises, leaders of trade unions, dependence of trade unions on will of employers. In the article events offer in relation to the improvement of adjusting of sociallabour relations under act of changes in the field of employment.

The Møller–Plesset perturbation revisited: origin of high-order divergences

Contrarily to what happens with the Epstein–Nesbet (EN) zeroth-order Hamiltonian, the Møller–Plesset (MP) perturbation operator has diagonal matrix elements, the expression of which is recalled. It is a balance between hole–hole and particle–particle repulsions on one hand and of hole–particle attractions on the other hand. For the double excitations, which dominate the correlation effects, the attractive terms prevail and the second-order MP energy is underestimated, at least for atoms of the first rows of the periodic table. It will be shown that when the perturbation expansion reaches multiple excitations, the diagonal terms of the MP perturbation operator may become larger than the zeroth-order MP excitation energy and creates an oscillating divergence of the series. Several situations of this type will be presented. This divergence is linked to the non-additivity of excitation energies, while this additivity is an underlying assumption for the linked cluster theorem and the coupled cluster method. This analysis may also explain why for heavy atoms the second-order MP energies overshoot the exact correlation energies.

Influence of Electric Field Coupling Model on the Simulated Performances of a GaN Based Planar Nanodevice

The performances of a two‐dimensional electron gas (2DEG) based planar nanodevice are studied by a two‐dimensional‐three‐dimensional (2D‐3D) combined model and an entirely 2D model. In both models, 2DEGs are depicted by 2D ensemble Monte Carlo (EMC) method. However electric field distributions in the devices are obtained by self‐consistently solving 2D and 3D Poisson equations for the 2D model and the 2D‐3D model, respectively. Simulation results obtained by both models are almost the same at low bias while showing distinguished differences at high bias. The 2D model predicts larger output current and slightly higher threshold voltage of Gunn oscillations. Although the fundamental frequencies of current oscillations obtained by both models are similar, the deviation of wave shape from sinusoidal waveform obtained by the 2D model is more serious than that obtained by 2D‐3D model. Moreover, results obtained by the 2D model are more sensitive both to the bias conditions and to the change of device parameters. Interestingly, a look‐like second harmonic oscillation has been observed at DC bias. We contribute the origin of divergences in simulation results to the different coupling path of electric field in the two models. And the second‐harmonic oscillations at DC bias should be the result of the appearance of concomitant oscillations beside the channel excited by strong electric‐field effects.

CCSD(T) Study of Dimethyl-Ether Infrared and Raman Spectra

CCSD(T) state-of-the-art ab initio calculations are used to determine a vibrationally corrected three-dimensional potential energy surface of dimethyl-ether depending on the two methyl torsions and the COC bending angle. The surface is employed to obtain variationally the lowest vibrational energies that can be populated at very low temperatures. The interactions between the bending and the torsional coordinates are responsible for the displacements of the torsional overtone bands and several combination bands. The effect of these interactions on the potential parameters is analyzed. Second order perturbation theory is used as a help for the understanding of many spectroscopic parameters and to obtain anharmonic fundamentals for the 3N - 9 neglected modes as well as the rotational parameters. To evaluate the surface accuracy and to verify previous assignments, the calculated vibrational levels are compared with experimental data corresponding to the most abundant isotopologue. The surface has been empirically adjusted for understanding the origin of small divergences between ab initio calculations and experimental data. Our calculations confirm previous assignments and show the importance of including the COC bending degree of freedom for computing with a higher accuracy the excited torsional term values through the Fermi interaction. Besides, this work shows a possible lack of accuracy of some available experimental transition frequencies and proposes a new assignment for a transition line. As an example, the transition 100 → 120 has been computed at 445.93 cm(-1), which is consistent with the observed transition frequency in the Raman spectrum at 450.5 cm(-1).

On the infrared behaviour of 3d Chern-Simons theories in $ \mathcal{N} = 2 $ superspace

We discuss the problem of infrared divergences in the N=2 superspace approach to classically marginal three-dimensional Chern-Simons-matter theories. Considering the specific case of ABJM theory, we describe the origin of such divergences and offer a prescription to eliminate them by introducing non-trivial gauge-fixing terms in the action. We also comment on the extension of our procedure to higher loop order and to general three-dimensional Chern-Simons-matter models.

On the origin of divergences in the coincidence probabilities in cavity photodetection experiments

The theory of photon correlation is an established part of quantum electronics. However, recently reported divergences in the theory of time correlated detection of photons show that important details of cavity photon statistics are still incompletely understood. The quantum jump superoperators of the SD photon counting model given by Srinivas and Davies (1981 J. Mod. Opt. 28 981–96 ) do not fulfil the assumption of the bounded interaction rate. This has raised doubts about the consistency of the SD photon counting model and especially about the existence of coincidence probability density (CPD) functions (Dodonov et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 99–108). In this work, we start from the first principles of the quantum trajectory theory and show how the different coincidence probability densities and coincidence probabilities (CPs) have to be calculated. CPDs derived by us are well defined, and CPs are finite and correctly normalized for all fields with finite photon number expectation value. Furthermore, we show that the SD model reproduces photon bunching and antibunching phenomena when consistent derivation for the second-order coherence degree is used.

Particle-number restoration within the energy density functional formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

Cuestiones actuales de la didáctica de las ciencias físicas en Francia : observaciones comparativas

The aim of this paper is to draw a first inventory of coincidences and differences of theoretical output between science and mathematics education. A comprehensive analysis of the origin and meaning of both coincidences and divergences is made.

Off-shell renormalization of the massive QED in the unitary gauge

Despite its simplicity, the unitary gauge is not a popular choice for practical loop calculations in gauge theories, due to the lack of off-shell renormalizability. We study the renormalization properties of the off-shell Green functions of the elementary electron fields in the massive QED, in order to elucidate the origin and structure of the extra ultraviolet divergences which exist only in the unitary gauge. We find that all these divergences affect the Green functions in a trivial way such that in coordinate space the off-shell Green functions are in fact multiplicatively renormalizable. This result may generalize to the abelian and non-abelian Higgs theories, for which the unitary gauge might bring much simplification to the loop calculations.

On the origin of divergences in massless QED2

We show that ultraviolet divergences found in fermionic Green functionsof massless QED2 have an essentially non-perturbative nature. Weinvestigate their origin both in the gauge invariant formalism (wherewe introduce Wess-Zumino fields to restore quantum gauge invariance)and in the gauge non-invariant formalism, mapping two different butequivalent mechanisms responsible for their appearance. We find the sameresults in both approaches, what contradicts a previous work of Jian-Ge,Qing-Hai and Yao-Yang, that found no divergences in the chiral Schwingermodel considered in the gauge invariant formalism.

Vacuum energy density fluctuations in Minkowski and Casimir states via smeared quantum fields and point separation

We present calculations of the variance of fluctuations and of the mean of the energy momentum tensor of a massless scalar field for the Minkowski and Casimir vacua as a function of an intrinsic scale defined by a smeared field or by point separation. We point out that contrary to prior claims, the ratio of variance to mean-squared being of the order unity is not necessarily a good criterion for measuring the invalidity of semiclassical gravity. For the Casimir topology we obtain expressions for the variance to mean-squared ratio as a function of the intrinsic scale (defined by a smeared field) compared to the extrinsic scale (defined by the separation of the plates, or the periodicity of space). Our results make it possible to identify the spatial extent where negative energy density prevails which could be useful for studying quantum field effects in worm holes and baby universe, and for examining the design feasibility of real-life `time-machines'. For the Minkowski vacuum we find that the ratio of the variance to the mean-squared, calculated from the coincidence limit, is identical to the value of the Casimir case at the same limit for spatial point separation while identical to the value of a hot flat space result with a temporal point-separation. We analyze the origin of divergences in the fluctuations of the energy density and discuss choices in formulating a procedure for their removal, thus raising new questions into the uniqueness and even the very meaning of regularization of the energy momentum tensor for quantum fields in curved or even flat spacetimes when spacetime is viewed as having an extended structure.

Orbital magnetic moment instability at the spin reorientation transition of Nd2Fe14B

Highly accurate soft-XMCD data recorded on a Nd2Fe14B single crystal, through the spin reorientation transition show that the average Fe orbital moment (a) is proportional to the macroscopic Fe anisotropy constant, and (b) diverges 15 K below the reorientation transition temperature. This divergence is indicative of a critical behavior and it is related to a tetragonal distortion. These results give experimental evidence of the mutual dependence between orbital moment, macroscopic magnetic anisotropy, and tetragonal distortion. Furthermore, it is argued that the critical behavior of the orbital moment is at the origin of similar divergences previously observed in Mossbauer and Hall-effect data.

Finite-temperature amplitudes in open-string systems.

I present an analysis of tree and one-loop finite-temperature amplitudes in open-string systems. Temperature is introduced through a recently developed real-time formalism for string thermodynamics and formal expressions for various cases are obtained. I point out the origin of divergences in the temperature-dependent amplitudes and show the emergence of the maximum (Hagedorn) temperature at the one-loop level for the open bosonic string and the open (type-I) superstring in the Ramond-Neveu-Schwarz formulation. I also discuss the problem of the tachyon stabilization by temperature effects as well as renormalization, symmetry, and supersymmetry breaking at finite temperature.

Common genetic pools between human populations.

A further inquiry on modern human origins, based on common genetic pool surveys of rigorously selected population samples and highly informative immunological polymorphisms, provides new evidence of an Occidental-Oriental population split as the origin of human gene pool divergences. The most likely ancestral genetic profile is discussed in the context of the debate raised by preliminary DNA restriction fragment length polymorphism studies, which contradict the conclusions drawn from classical blood group analyses.