Ordinary Field Research Articles

Equilibrium States in Thermal Field Theory and in Algebraic Quantum Field Theory

In this paper we compare the construction of equilibrium states at finite temperature for self-interacting massive scalar quantum field theories on Minkowski spacetime proposed by Fredenhagen and Lindner with results obtained in ordinary thermal field theory, by means of real time and Matsubara formalisms. In the construction of this state, even if the adiabatic limit is considered, the interaction Lagrangian is multiplied by a smooth time cut-off. In this way the interaction starts adiabatically and the correlation functions are free from divergences. The corresponding interaction Hamiltonian is a local interacting field smeared over the interval of time where the chosen cut-off is not constant. In order to cope with this smearing, the Matsubara propagator needs to be modified. We obtain an expansion of the correlation functions of the interacting equilibrium state as a sum over certain type of graphs with mixed edges, some of them correspond to modified Matsubara propagators and others to propagators of the real time formalism. An integration over the adiabatic time cut-off is present in every vertex. However, at every order in perturbation theory, the final result does not depend on the particular form of the cut-off function. The obtained graphical expansion contains in it both the real time formalism and the Matsubara formalism as particular cases. Finally, we show that a particular factorisation which is used to derive the ordinary real time formalism holds only in special cases and we present a counterexample. We conclude with the analysis of certain correlation functions and we notice that corrections to the self-energy in a $\lambda\phi^4$ at finite temperature theory are expected.

Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation

We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomial associated with a non-reflexive difference-differential ideal in the algebra of difference-differential polynomials with several basic derivations and one translation. In particular, we obtain a new proof and a method of computation of the dimension polynomial of a non-reflexive prime difference ideal in the algebra of difference polynomials over an ordinary difference field. As a consequence, it is shown that the reflexive closure of a prime difference polynomial ideal is the inverse image of this ideal under a power of the basic translation. We also discuss applications of our results to the analysis of systems of algebraic difference-differential equations.

Non-Abelian basis tensor gauge theory

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.

Matter perturbation in coupled scalar field cosmology

A universe containing a coupled scalar field would have different dynamical evolution compared to uncoupled cases. Significant differences are expected to emerge during matter dominated era, where scalar field density mimics how matter density evolves, by becoming subdominant. Analysis of the dynamics was investigated both analytically and numerically through phase plane method, and we obtained two attractor solutions which are compatible to a late time cosmic acceleration as the ending of matter dominated era. Ordinary scalar field triggers an acceleration with stable attractor solution which converges to ωϕ = ωeff ≈ −1. Whereas, phantom scalar field allows negative values for its own energy (ωeff ˂ −1 and Ωϕ ˂ 0); however this is not stable, therefore it will be caught by attractor solution which is stable to ωϕ = ωeff ≈ −1. In addition, we found cosmological parameters generated from both analytical and numerical calculations, i.e. ωϕ, Ωϕ and ωeff, by assuming a flat universe. The existence of a coupling constant Q between scalar field and matter induces different structure growth compared to uncoupled cases and standard cold dark matter (CDM) model. During matter dominated era, ordinary scalar field induces growth of structures so that it becomes faster than the standard model does, whereas phantom scalar field slows down the growth of structures. During scalar field dominated era (far in the future), we obtained that formed structures or density contrasts will decay in a similar way as in uncoupled cases, whereas following phantom scenario, the decay of formed structures occurs faster and more significant. This result is associated to background dynamics which shows that big rip will be the relevant fate of our universe.

Symmetric moving frames

A basic challenge in field-guided hexahedral meshing is to find a spatially-varying frame that is adapted to the domain geometry and is continuous up to symmetries of the cube. We introduce a fundamentally new representation of such 3D cross fields based on Cartan's method of moving frames. Our key observation is that cross fields and ordinary frame fields are locally characterized by identical conditions on their Darboux derivative. Hence, by using derivatives as the principal representation (and only later recovering the field itself), one avoids the need to explicitly account for symmetry during optimization. At the discrete level, derivatives are encoded by skew-symmetric matrices associated with the edges of a tetrahedral mesh; these matrices encode arbitrarily large rotations along each edge, and can robustly capture singular behavior even on coarse meshes. We apply this representation to compute 3D cross fields that are as smooth as possible everywhere but on a prescribed network of singular curves---since these fields are adapted to curve tangents, they can be directly used as input for field-guided mesh generation algorithms. Optimization amounts to an easy nonlinear least squares problem that behaves like a convex program in the sense that it always appears to produce the same result, independent of initialization. We study the numerical behavior of this procedure, and perform some preliminary experiments with mesh generation.

Tight binding approach for cuprate superconductors–Energy of the mean field and the correlation

We construct a mean field theory different from the wave vector representation, based on the observation that the ordinary mean field theory for superconductivity involves an inconsistency in the description of high Tcd-wave superconductivity. By using a cell- and ion-position (site position) representation, we obtain a basis for the tight-binding approximation (TBA) of the energy gap parameter and the energy of the pair condensate system. The mean field Hamiltonian is not diagonalized exactly by the Bogoliubov transformation, but a diagonalizable Hamiltonian may be defined by a truncation of that. A modified BCS model is introduced accompanying this Hamiltonian. We calculate the energy of the mean field and, moreover, the correlation energy of the condensate system in the TBA. We use the Gaussian orbital method to show that the gap parameter has a d-wave-like node structure in the form defined in the wave vector representation, but the gap in the site position representation and the quasiparticle energy do not have a node structure. The correction of the gap parameter by the off-site pair interaction is shown to be the first-order perturbation and the correction of the mean field energy is the second-order perturbation. The ratio of the correlation energy to the mean field energy is on the order of the carrier concentration in this TBA.

Reduced percolation threshold of multi-walled carbon nanotubes/polymer composites by filling aligned ferromagnetic particles

Conductive polymer composites, consisting of multi-walled carbon nanotubes and a small amount of carbonyl iron particles, are fabricated under an ordinary magnetic field, to form anisotropic microstructures. The alignment of carbonyl iron particles will change the structure of a multi-walled carbon nanotube network and consequently the electrical properties of conductive polymer composites. In this research, we focus on the effect of the anisotropic microstructures on the electrical properties of the composites, especially on the percolation threshold and electrical resistivity. Monte Carlo simulations for three-dimensional stick percolation systems are performed to predict the percolation threshold of the anisotropic conductive polymer composites in terms of orientation distribution of multi-walled carbon nanotubes. In addition, an eight-chain model is proposed to investigate the influence of the anisotropic distribution of multi-walled carbon nanotubes on the electrical resistivity of the composites. It is predicted that the percolation threshold could be reduced from 0.70 vol% for the isotropic composites to 0.49 vol% for the anisotropic composites. Meanwhile, the electrical resistivity of the anisotropic composites is about 10%–20% of that of the isotropic composites when the volume fraction of multi-walled carbon nanotubes is higher than the percolation threshold. The simulation results are compared with the experimental study results that show a very similar behavior although there are some deviations in the values.

Test-field limit of metric nonlinear gravity theories

In the framework of alternative metric gravity theories, it has been shown by several authors that a generic Lagrangian depending on the Riemann tensor describes a theory with 8 degrees of freedom (which reduce to 3 for f(R) Lagrangians depending only on the curvature scalar). This result is often related to a reformulation of the fourth-order equations for the metric into a set of second-order equations for a multiplet of fields, including – besides the metric – a massive scalar field and a massive spin-2 field (the latter being usually regarded as a ghost): this is commonly assumed to represent the particle spectrum of the theory. In this article we investigate an issue which does not seem to have been addressed so far: in ordinary general-relativistic field theories, all fundamental fields (i.e. fields with definite spin and mass) reduce to test fields in some appropriate limit of the model, where they cease to act as sources for the metric curvature. In this limit, each of the fundamental fields can be excited from its ground state independently from the others (which does not happen, instead, as long as the fields are coupled through the gravitational interaction). We thus address the following question: does higher-derivative gravity admit a test-field limit for its fundamental fields? It is easy to show that for a generic f(R) theory (carrying 3 d.o.f.) the test-field limit does exist; then, we consider the case of Lagrangians depending on the full Ricci tensor, relying on a previous analysis published several years ago. We show that, already for a quadratic Lagrangian, the constraint binding together the scalar field and the massive spin-2 field does not disappear in the limit where they should be expected to act as test fields. A proper test-field limit exists only for a particular choice of the coefficients in the Lagrangian, which cause the scalar field to disappear (so that the resulting model has only 7 d.o.f.). We finally consider the possible addition of an arbitrary function of the quadratic invariant of the Weyl tensor, C^{alpha }{}_{beta mu nu }C_{alpha }{}^{beta mu nu }, showing that the appearance of the Weyl tensor does not add physical degrees of freedom (in accordance to the known results for Lagrangians depending on the full Riemann tensor) and the resulting model with 8 d.o.f. still lacks a proper test-field limit: the differential constraints between the fundamental fields do not cancel out when gravitational interaction is suppressed. We argue that the lack of a test-field limit for the dynamics of the fundamental fields may constitute a serious drawback of the full 8 d.o.f. higher-order gravity models, which is not encountered in the restricted 7 d.o.f. or 3 d.o.f. cases.

Helical‐Like 3D Ultrathin Piezoelectric Element for Complicated Ultrasonic Field

AbstractThe developments of personalized medicine, ultrasound imaging, and contactless “microscopic handle” techniques are pushing ultrasonic transducers toward features of high frequency, device miniaturization, and even novel function. However, the conventional ultrasonic transducer has severely limited the development of novel ideas for applications due to its ordinary ultrasonic field. Although transducer arrays and monolithic acoustic holograms are capable of producing the complicated ultrasonic field, it is still difficult to achieve high frequency, device miniaturization, and novel function simultaneously. Here, a simple but effective approach is introduced that aims at reconstructing the complicated and high‐frequency ultrasonic field via a compact single‐element ultrasonic transducer. The 3D ultrathin piezoelectric element with a complex configuration is demonstrated theoretically and experimentally to produce the desired complicated ultrasonic field. With helical‐like configuration, the single‐element ultrasonic transducer offers efficient noncontact trapping and manipulation of suspended microparticles and biological cells. Moreover, its strong trapping capability leads to the 3D stacking of microparticles, which is a novel and interesting phenomenon achieved by a single‐element ultrasonic transducer. This work brings the possibility of a complicated ultrasonic field for achieving novel high‐frequency ultrasound applications through the design of smart structure ultrathin piezoelectric materials.

Simulation of Melt Viscosity Effect on the Rate of Solidification in Polymer

Phase field model has been successfully derived from ordinary metal phase field equation to simulate the behavior of semi-crystalline polymer solidification phenomenon. To obtain the polymer phase field model, a non-conserved phase field equation can be expanded to include the unique polymer parameters, which do not exist in metals, for example, polymer melt viscosity and diffusion coefficient. In order to expand this model, we include free energy density and non-local free energy density based on Harrowel-Oxtoby and Ginzburg-Landau theorem for polymers. The expansion principle for a higher order of binary phase field parameter was employed to obtain fully modified phase field equation. To optimize the final properties of the products, the solidification phenomenon in polymers is very important. Here, we use our modified equation to investigate the effect of melt viscosity on the rate of solidification by employing ordinary differential equation numerical methods. It was found that the rate of solidification is related to the melting temperature and the kinetic coefficient.

A new kind of quantum field theory of (n – 1)-dimensional defects in 2n dimensions

I describe a project to open a new territory of quantum field theory where the fields live not on a space–time manifold but on certain complete metric spaces of (n − 1)-dimensional objects (defects) in a 2n-dimensional space-time M. These metric spaces are ‘quasi Riemann surfaces’; they are formally analogous to Riemann surfaces. Every construction of a 2d conformal field theory (CFT) is to give an analogous construction of a CFT on the quasi Riemann surfaces, and thereby a cft on M. The global symmetry group of the 2d CFT becomes a local gauge symmetry. Ordinary local quantum fields in space–time are constructed by restricting to small objects. The project is based on writing the free n-form in 2n dimensions as the 2d Gaussian model on the quasi Riemann surfaces.

Reconstruction of energy conditions from observations and implications for extended theories of gravity

The attempt to describe the recent accelerated expansion of the Universe includes different propositions for dark energy models and modified gravity theories. Establish their features in order to discriminate and even rule out part of these models using observational data is a fundamental issue of cosmology. In the present work we consider a class of extended theories of gravity (ETG) that are minimally coupled to the ordinary matter fields. In this context, and assuming a homogeneous and isotropic spacetime, we derive the energy conditions for this ETG class. We then put constraints on these conditions using a model-independent approach to reconstruct the deceleration function along with the Joint Light-curve Analysis (JLA) supernova sample, 11 baryon acoustic oscillation and 22 cosmic-chronometer measurements. We also consider an additional condition imposing the strong energy condition only on the ordinary matter. This is to guarantee the presence of only attractive matter in the energy–momentum tensor, at least in the redshift range of the observations, i.e., the recent accelerated expansion of the Universe is due solely to the modifications in the gravity theory. The main result of this work is a general reconstruction of the energy conditions valid for every considered ETG.

METHOD FOR ESTIMATING GAS REMAINING IN A PLATE IN THE FORM OF FREE GAS SATURATION ZONES

As it is known, when developing an oil reservoir in the dissolved gas mode, not all of the gas released from the oil comes to the surface, part of it remains in the reservoir in the form of free gas saturation zones. Not accounting for this gas can lead to a distortion of the actual situation that has developed in the reservoir and the inefficiency of subsequent measures taken to develop it. In this regard, questions arise about how to determine the presence of gas remaining in the reservoir and how to assess its amount. This article is devoted to solving the questions posed. An example is the Hassi-Mesaud field, located in Northern Africa. During the operation of the field, a weak activity of circulating water and a rapid drop in reservoir pressure were noted, which led to intensive expansion of the gas cap and the release of dissolved gas from oil. The considered field is characterized by a sharp heterogeneity and an extremely unfavorable ratio of phase permeabilities of gas and oil. If in ordinary fields the equality of oil and gas production rates in reservoir conditions is achieved at a gas saturation of 7 - 17 %, then in the field under consideration this condition is achieved at a gas saturation of 2.5 %. The task of determining the presence of free gas saturation zones was reduced to constructing a graph of the relationship between the ratio of the phase permeabilities of oil and gas and gas saturation. Such dependence was built for data obtained on the basis of core studies and field studies. The analysis of the constructed curves made it possible not only to determine the presence or absence of gas in the reservoir, but also to make an approximate assessment of the share of this gas in the total volume of the total gas released from oil.

Влияние формы канала на амплитуду случайных телеграфных шумов в подпороговой области беспереходного FinFET-транзистора

In this work it is simulated the random telegraph noise signal amplitude dependence on gate voltage overdrive for silicon on insulator junctionless FinFET transistor with fin cross section in rectangle and trapeze form. It is shown in subthreshold region the noise signal amplitude is lower in case of trapeze cross section of the fin. Besides it approximately at the same condition the noise signal amplitude is essentially lower in junctionless fin field effect transistor than in bulk, fully depleted silicon on insulator and ordinary fin field effect transistors.

Technological Features of the Renewed System of Selective Dissemination of Information in the Library for Natural Sciences of the RAS

The wide spectrum of full text and bibliographic information resources (e. g. Web of Science, Scopus), which Library for Natural Sciences of the Russian Academy of Sciences (LNS RAS) had in its subscription for the last few years, was a ground for the autors' efforts in developing of the modern system of selective dissemination of information (SDI system). At the same time, acquisition of information sources on traditional media has been steadily decreasing in recent years.Sources of bibliographic information in this SDI system are bibliographic databases Web of Science and Scopus, and full-text platforms of foreign scientific publishers (currently — several dozen, including John Wiley & Sons, Springer Nature and ScienceDirect).The users of the SDI system have opportunity to get two kinds of service: the first one is informing on the current issues of the scientific journals which are preselected by user himself; the second one is the thematic informing based on the keywords of user thematic requests. This SDI system has the important feature that distinguishes it from traditional definition of SDI systems: we do not restrict either lists of journals reported by users nor the bibliographic sources in thematic sets by the list of full text sources available via library’s subscription. The only condition for including specific journal in the SDI system for the first kind of service or including the bibliographic source in thematic sets for the second kind of service is existing of the source as electronic web entity. If user has made order for full text material from contents/thematic information set, the library retrieves such full text material via all available ways beginning with library’s subscription and finishing with interlibrary loan.We have selected e-mail sending of personalized information sets for our users, as it was the mode selected as preferable mode by our users themselves. Personalized information sets include ordinary fields of bibliographic record (incl. abstracts if available in protosource) and some fields for increasing navigation options of records: link to full text via DOI, link for article record in Scopus and PubMed, information about library’s subscription for source where specific record is published.

Signal propagation on κ -Minkowski spacetime and nonlocal two-point functions

We study the propagation of quantum fields on $\kappa$-Minkowsi spacetime. Starting from the non-commutative partition function for a free field written in momentum space we derive the Feynman propagator and analyze the non-trivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such singularity structure result in a deformed field propagation which can be alternatively described in terms of an ordinary field propagation determined by a source with a blurred spacetime profile. We show that the $\kappa$-deformed Feynman propagator can be written in terms of vacuum expectation values of a commutative non-local quantum field. For sub-Planckian modes the $\kappa$-deformed propagator corresponds to the vacuum expectation value of the time-ordered product of non-local field operators while for trans-Plankian modes this is replaced by the Hadamard two-point function, the vacuum expectation value of the anti-commutator of non-local field operators.

Unitarity of the box diagram

The complete proof of cutting rules needed for proving perturbative unitarity of quantum field theories usually employs the largest time equation or old fashioned perturbation theory. None of these can be generalized to string field theory that has non-local vertices. In arXiv:1604.01783 we gave a proof of cutting rules in string field theory, which also provides an alternative proof of cutting rules in ordinary quantum field theories. In this note we illustrate how this works for the box diagram of ϕ4 field theory, avoiding the contributions from anomalous thresholds.

Quantum Vacuum Fluctuations in a Chromomagnetic-Like Background

In this paper we study the effects associated to quantum vacuum fluctuations of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static and homogeneous chromomagnetic-like background field, at zero temperature. We use periodic and antiperiodic boundary conditions in order to calculate the Casimir energy by means of the frequency sum technique and of the regularization method based on zeta functions, analyzing its behavior in the weak and strong coupling regimes. We compare the obtained results with the similar ones found for scalar and spinor fields placed in an ordinary magnetic field background. We show that only in the weak coupling regime the non-trivial topology of the system encoded in the antiperiodic boundary conditions changes the nature of the Casimir force with respect to the periodic ones. Considering the weak coupling scenario, we show that the introduction of a third polarization state in the perturbations makes manifest the effects on the Casimir energy due to the coupling with the chromomagnetic-like background field, for both the boundary conditions. Finally, in the strong coupling regime, in which the quantum vacuum is not stable due to the Nielsen-Olesen instabilities, we evaluate the effects of a compact extra dimension on its stabilization.

Learning about forest ownership and management issues in Europe while travelling: The Travellab approach

Forest management, with its diverse land-use and institutional pressures, can be considered a “wicked problem”. Transdisciplinarity and social learning are considered relevant approaches of investigating “wicked problems” because they favour creative solutions, stakeholder involvement and the reframing of problems. Taking this into account, participant researchers in the COST Action FACESMAP developed the Travellab approach to enhance their understanding of forest ownership, management and policy across Europe. The Travellab favours interaction in a structured way, collection and analysis of the information discussed, reflection about the process and the topics learnt, and reframing of the discussion topics and of the interaction techniques. This article explores the effectiveness of the Travellab to enhance researchers' learning during interactions with stakeholders. The evidence presented indicates that the Travellab improved joint learning among researchers and enriched the quality of knowledge transferred, but did not effectively support knowledge exchange. Nevertheless, the Travellab added greater value to FACESMAP field visits when compared to ordinary field trips embedded in project meetings. The implementation of the Travellab approach in research projects of all sizes and international networks to improve group and individual learning is, therefore, highly recommended.

Unitary Quantization and Para-Fermi Statistics of Order 2

A connection between a unitary quantization scheme and para-Fermi statistics of order 2 is considered. An appropriate extension of Green's ansatz is suggested. This extension allows one to transform bilinear and trilinear commutation relations for the annihilation and creation operators of two different para-Fermi fields $\phi_{a}$ and $\phi_{b}$ into identity. The way of incorporating para-Grassmann numbers $\xi_{k}$ into a general scheme of uniquantization is also offered. For parastatistics of order 2 a new fact is revealed, namely, the trilinear relations containing both the para-Grassmann variables $\xi_{k}$ and the field operators $a_{k}$, $b_{m}$ under a certain invertible mapping go over into the unitary equivalent relations, where commutators are replaced by anticommutators and vice versa. It is shown that the consequence of this circumstance is the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green's components of the operators $a_{k}$, $b_{m}$ is constructed in an explicit form that enables us to reduce the initial commutation rules for the components to the normal commutation relations of ordinary Fermi fields. A nontrivial connection between trilinear commutation relations of the unitary quantization scheme and so-called Lie-supertriple system is analysed. A brief discussion of the possibility of embedding the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is provided.