Field Theoretical Approach Research Articles

Dynamics of a noninteracting colloidal fluid in a quenched Gaussian random potential: a time-reversal-symmetry-preserving field-theoretic approach

We develop a field-theoretic perturbation method preserving the fluctuation–dissipation relation (FDR) for the dynamics of the density fluctuations of a noninteracting colloidal gas plunged in a quenched Gaussian random field. It is based on an expansion about the Brownian noninteracting gas and can be considered and justified as a low-disorder or high-temperature expansion. The first-order bare theory yields the same memory integral as the mode-coupling theory (MCT) developed for (ideal) fluids in random environments, apart from the bare nature of the correlation functions involved. It predicts an ergodic dynamical behavior for the relaxation of the density fluctuations, in which the memory kernels and correlation functions develop long-time algebraic tails. An FDR-consistent renormalized theory is also constructed from the bare theory. It is shown to display a dynamic ergodic–nonergodic transition similar to the one predicted by the MCT at the level of the density fluctuations, but, at variance with the MCT, the transition does not fully carry over to the self-diffusion, which always reaches normal diffusive behavior at long time, in agreement with known rigorous results.

Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading

We study fluctuation effects in the two-species reaction-diffusion systemA+B→ Ø andA+A→ (Ø,A). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays inddimensions with the distanceraccording to a power-lawr−d−σ. For anomalous diffusion (including Lévy flights) the critical dimensiondc=σdepends on the control parameterσ, 0<σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind theBparticle density calculation.

Extreme Strain Fluctuations in Polycrystalline Materials

The stochastic structure of polycrystalline materials causes a high inhomogeneity of the kinematic and force fields in grains of materials and large fluctuations of these fields. The inhomogeneity and fluctuations are insignificant in some cases, but they become crucial in the study of various critical phenomena whose occurrence strongly depends on the type of material microstructure. Fluctuations mainly arise due to the elastic interaction of grains, which has a long-range effect. Therefore, it is necessary to account for the interaction of a large number of grains, which is difficult to do using conventional methods (direct computer modeling and others). In the present paper, inhomogeneous mesostrain fluctuations in grains of polycrystalline materials were estimated using a field-theoretical approach to a boundary-value problem of microheterogeneous material deformation. Particular attention is paid to the calculation of extreme fluctuations that are important for some critical phenomena, such as, e.g., crack initiation under gigacycle fatigue when the macrostress amplitude and the mean stresses in grains are much lower than the quantities included in any macroscopic damage or fatigue criteria. Phe maximum mesostrains in grains can exceed several times the macrostrains. Extreme fluctuations in a grain are generated in grain clusters of specific configuration. Phe applied approach makes it possible to predict patterns of such clusters. Extreme fluctuations in the bulk grains of a polycrystalline body are much higher than in the surface grains, due to which the behavior of the material surface layers and bulk volumes is different. Quantitative data are given for the case of uniaxial tension of polycrystalline zinc.

‘Alleen vette prijzen doen ertoe’

Abstract Literary prizes have become indispensable to the literary field and have developed into one of its most high-profiled phenomena. They promote competing forms of consecration; intersect in the dynamic relationships of actors and institutions; and contribute to defining the parameters of literature and literary culture. This article investigates the relationship between literary awards and literary criticism in the Netherlands from both a quantitative and qualitative perspective, whilst drawing on field-theoretical approaches to literature. As literary critics consecrate some authors but not others, so they determine to a large extent which literary prizes matter and which do not. This article charts the rise of literary awards on the Dutch literary field, and the critical attention these prizes have received. It researches which prizes are consecrated (and why), and in which ways literary criticism has written about those awards over the course of years.

Gauge theory of strongly-correlated symmetric topological Phases

In the presence of symmetry-protection, topological invariants of topological phases of matter in free fermion systems, e.g., topological band insulators, can be directly computed via the properties of band structure. Nevertheless, it is usually difficult to extract topological invariants in strongly-correlated topological phases of matter in which band structure is not well-defined. One typical example is the fractional quantum Hall effect whose low-energy physics is governed by Chern-Simons topological gauge theory and Hall conductivity plateaus involve extremely fruitful physics of strong correlation. In this article, we focus on intrinsic topological order (iTO), symmetry-protected topological phases (SPT), and symmetry-enriched topological phases (SET) in boson and spin systems. Through gauge field-theoretical approach, we review some research progress on these topological phases of matter from the aspects of projective construction, low-energy effective theory and topological response theory.

The variety of approaches to the problem of the derivation of Dirac equation

Purpose. The Dirac equation is one of the fundamental equations of modern theoretical physics. It is in service more than 90 years (1928–2018). The application today is much wider than the areas of quantum mechanics, quantum field theory, atomic and nuclear physics, solid state physics. The successful derivation of some equation of mathematical physics is the first step to successful application. In such process the essence of the corresponding model of nature, the mathematical principles and the physical foundations are visualized. Here we deal with the different approaches to the problem of the Dirac equation derivation. Methods. The quantum-mechanical, quantum field-theoretical, group-theoretical, algebraic, symmetrical, statistical, stochastical and numerical approaches are used. Results. The 26 different ways of the Dirac equation derivation are presented. The various physical principles and mathematical formalisms are used. Three original approaches of the authors to the problem are given. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic quantum mechanics of the fermion-antifermion spin s = 1/2 doublet. In some sense the role of the Dirac equation today is demonstrated. Conclusions. The original investigation of the problem of the Dirac equation derivation is presented. The different approaches, which are based on the various mathematical and physical principles, are considered (26 methods). Therole of the scientists from Uzhhorod is shown. The importance of place of the Dirac equation in modern theoretical physics is discussed.

Black Hole Suns: Binarism and Gravity in Cultural Fields

Sociologicial analyses of artistic practice have long drawn on theoretical traditions grounded in binaries and dualisms. Such analytical strategies, exemplified here by field theoretical approaches, center art objects and their movements in and across markets, where binaristic visions of art worlds do offer significant leverage. But when the analyst moves away from markets for art objects and looks to artistic practices the binaristic lens provides, at best, a blurred image with meaningful blind spots. This article suggests an alternative vision of artistic practice —one based on gravity rather than polarity—that captures the ways individuals and their actions make sense in a specific universe of meaning without forcing them into fundamentally competitive and economistic relationships. It leverages findings enabled by a unique sampling strategy in a four year study of visual artists in the United States to illuminate some limitations of binary theoretical frameworks, and outlines a generative alternative to dualism that promotes new analytical and theoretical directions for sociological analyses of artists and artistic practice. This alternative model provides new leverage on four persistent issues in analyses of artistic work: cultural change in occupational fields; actors’ attempts to manage overlapping but incommensurate forms of recognition, reputation, attention, and success; the persistent hegemony of markets for objects in both vernacular and sociological understandings of artistic practice; and questions of visibility and legitimacy central to understanding boundary formation and boundary work in creative fields. The gravitational metaphor promotes a distict set of strategies for the study of artistic work as well as other nontraditional occupations.

Elastoplastic interaction of grains in polycrystalline materials

A new method is developed for solving boundary value problems of elastoplastic deformation of polycrystalline materials based on the field-theoretical approach. The boundary value problem for inhomogeneous global strain fields in differential form is transformed into a system of integral equations for mesostrain tensors in grains. In this approach, strain at any point of any grain represented as a superposition of homogeneous macrostrain and contributions of interactions with strain in given grain and all another grains of polycrystalline body . It is shown that the effects of the interaction of strains in polycrystal grains can be described using tensors of the fourth rank. This tensor has 36 independent components. The interactions are additive in nature, that drastically simplifies the solution of some problems, for example, search for extreme microstructures of a polycrystal in which critical localized phenomena arise, such as nucleation of the first plastic slips occur. Constitutive equations of deformation type are used for whole body and separate grains. A model of elastoplastic deformation of single crystals of grains is constructed. The physical mechanisms of plastic deformation are shifts in slip systems of crystals. General expressions are obtained for calculating the secant modules of single crystals for any multiaxial deformation. To solve systems of integral equations for mesostrains in grains the perturbation theory upon intergrains interaction used. Nonlinear systems of equations for plastic strains are solved by the iteration method. The features of the elastoplastic interaction of grains are theoretically investigated. The intensity of the elastoplastic interaction depends on the deformed state of the grains. For two identical grains, the elastoplastic interaction of the pair is several times more intense than the elastic one. In this case, the effect of plastically deformed grain on elastically deformed grain is much higher than the inverse effect. An increase in the intensity of interaction with the development of plastic deformations leads to the effect of homogenization of mesodeformations. Computational experiments were performed using polycrystalline titanium as an example.

Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for the one-dimensional δ -function potential

In contrast with the 3D result, the Beth-Uhlenbeck (BU) formula in 1D contains an extra -1/2 term. The origin of this -1/2 term is explained using a spectral density approach. To be explicit, a delta-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in 1D. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the delta-function potential, the method and result are valid for more general potentials. Additionally, the 1D Levinson's theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in 1D have a universal source: a pole at zero energy. Similar calculations using quantum field theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (appendix A).

Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics.

We study the nature of the phase diagram of three-dimensional lattice models in the presence of non-Abelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with N_{f} flavors, characterized by a non-Abelian SU(N_{c}) gauge symmetry. For N_{f}≥2 (multiflavor case), it presents two phases separated by a transition line where a gauge-invariant order parameter condenses, being associated with the breaking of the residual global symmetry after gauging. The nature of the phase transition line is discussed within two field-theoretical approaches, the continuum scalar chromodynamics, and the Landau-Ginzburg-Wilson (LGW) Φ^{4} approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for N_{f}=2, 3 and N_{c}=2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases.

Field-theoretic approach to large-scale structure formation

We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in longitudinal gauge. We integrate out the gravitational constraint fields and arrive at a non-local action which is only specified in terms of the dynamical degrees of freedom. In order to make this framework closer to the classical particle description, we construct the corresponding 2PI effective action truncated at two loop order for a non-squeezed state without field expectation values. We contrast the dynamical description of the coincident time phase-space density to the standard Vlasov description of cold dark matter particles and identify momentum and time scales at which linear perturbation theory will deviate from the standard evolution.

Journalistic autonomy and frame sponsoring. Explaining Japan’s “nuclear blind spot” with field theory

Studies of Japanese media have noted a “nuclear blind spot” in the Japanese press before the Fukushima accident 2011. In contrast to other countries the civil use of nuclear power was only rarely criticized. This blind spot has been explained either with cultural factors like ideas of the relation between the environment and humans or with political control of media through press clubs. In the paper a frame analysis of three Japanese newspapers’ nuclear power reporting is combined with a field-theoretical approach. To map the journalistic field descriptions of journalistic professional ideals and measures of journalistic autonomy on the individual and company level are analysed together. In the commercial newspapers, more journalists see themselves as “educators” of the public. In newspapers with more field-specific symbolic capital, more journalists tend towards a critical ideal. It is shown how critical journalists were subject to organized pressure from the nuclear industry before 2011 and it is argued that this is a key factor in explaining the “nuclear blind spot”. To make visible such restrictions of autonomy is a potential strength of an orthodox Bourdieusian version of field theory based on the concepts of symbolic capital and autonomy. The combined analysis of capital and self-perceptions could be a way to bridge the explanatory gap between journalistic self-perceptions (role models) and journalistic practice.

Description of processes passing at finite space-time intervals in the framework of quantum field theory

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most know phenomena of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes demands that the rules of passing to the momentum representation in the Feynman diagram technique be adjusted in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets: both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We demonstrate the validity of the formalism by applying it to describing the decay of an unstable particle and neutrino oscillations. It is shown that the considered approach correctly reproduces the known results.

X(3872) as virtual companion pole of the charm–anticharm state χc1(2P)

We study the spectral function of the axial-vector charmonium state [Formula: see text] coupled to [Formula: see text] mesons, by employing a quantum field theoretical approach: a pronounced enhancement close to the [Formula: see text] threshold, to be identified with the [Formula: see text], emerges. In the complex plane we find two poles: a pole for the broad seed state [Formula: see text], and — in the easiest scenario — a virtual pole for the [Formula: see text]. Thus, our approach describes both the seed state and the dynamically generated [Formula: see text] simultaneously. In particular, it explains the most prominent, both molecular-like and quarkonium-like, features of the [Formula: see text]: its very small width (the decay into [Formula: see text] is predicted to be about 0.5 MeV), the enhanced radiative decay into [Formula: see text] with respect to [Formula: see text], and the isospin breaking decay into [Formula: see text] (thanks to [Formula: see text] loops mediating this decay channel). At the same time, we aim to determine the pole position and the properties of the charmonium seed state: quite interestingly, even if a pole is always present, it is possible that there is no peak corresponding to this state in the spectral function, thus potentially explaining why the corresponding resonance could not yet be seen in experiments.

Quantum gravitational corrections to a star metric and the black hole limit

In this paper we consider the full set of quantum gravitational corrections to a star metric to second order in curvature. As we use an effective field theoretical approach, these corrections apply to any model of quantum gravity that is based on general coordinate invariance. We then discuss the black hole limit and identify an interesting phenomenon which could shed some light on the nature of astrophysical black holes: while star metrics receive corrections at second order in curvature, vacuum solutions such as black hole metrics do not. What happens to these corrections when a star collapses?

Individuality, quasi-sets and the double-slit experiment

Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is on the double-slit experiment, a major physical phenomenon which was never modeled from a quasi-set-theoretic point of view. The double-slit experiment strongly motivates the concept of degrees of indistinguishability within a field-theoretic approach, and that notion is simply missing in $\cal Q$. Nevertheless, other physical situations may eventually demand a revision on quasi-set theory axioms, if someone intends to use it in the quantum realm for the purpose of a clear discussion about non-individuality. I use this opportunity to suggest another way to cope with identity in quantum theories.

Coherence length of neutrino oscillations in a quantum field-theoretical approach

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most known processes of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes requires one to adjust the rules of passing to the momentum representation in the Feynman diagram technique in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets, both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We consider neutrino oscillation processes, where the neutrinos are produced in three-particle weak decays of nuclei and detected in the charged-current interaction with nuclei or in the charged- and neutral-current interactions with electrons. Particular examples are considered and it is shown that the momentum spread of the produced neutrinos and the energy dependence of the differential cross section of the detection process result in the suppression of neutrino oscillation, which is characterized by a coherence length specific for a pair of production and detection processes. This coherence length turns out to be much less than the coherence length in the standard quantum-mechanical approach defined by the quantum uncertainty of neutrino momentum.

Generalized route to effective field theories for quantum systems with local constraints

Effective models featuring hard local constraints describe several strongly correlated electronic systems that exhibit interesting and exotic behavior from emergent gauge symmetries to deconfined criticality and topological order. A systematic field-theoretic approach to such models remained elusive to date, with effective theories constructed from physical insight. Here, the authors propose a general large-$S$ path-integral formalism to obtain field theories for hard constrained Hamiltonians. They demonstrate its potential by performing a systematic study of quantum dimer models, including such on nonbipartite lattices.

Self-Consistent Field Theory Coupled with Square Gradient Theory of Free Surfaces of Molten Polymers and Compared to Atomistic Simulations and Experiment

A self-consistent field (SCF) theoretic approach, using a general excess Helmholtz energy density functional that includes a square gradient term, is derived for polymer melt surfaces and implemented for linear polyethylene films over a variety of temperatures and chain lengths. The formulation of the SCF plus square gradient approximation (SGA) developed is generic and can be applied with any equation of state (EoS) suitable for the estimation of the excess Helmholtz energy. As a case study, the approach is combined with the Sanchez–Lacombe (SL) EoS to predict reduced density profiles, chain conformational properties, and interfacial free energies, yielding very favorable agreement with atomistic simulation results and noticeable improvement relative to simpler SCF and SGA approaches. The reduced influence parameter invoked in the SGA to achieve accurate density profiles and interfacial free energies is consistent with the definition of Poser and Sanchez, J. Colloid Interface Sci. 1979, 69, 539–548. The ...

Supersymmetry in the Insulating Phase of a Chain of Majorana Cooper Pair Boxes

The charging energy U of a small superconducting island containing Majorana zero modes-a Majorana Cooper-pair box-induces interactions between the Majorana zero modes. Considering a chain of many such boxes, a topological superconductor-insulator transition occurs when U is much larger than the transfer matrix element t between the boxes. In this Letter, we focus on the insulting phases occurring in this regime. We show that there are several competing insulating phases, and that the transition between them is described by a supersymmetric field theory with a central charge c=7/10. We obtain this result by mapping the model to a spin-1 system and through a field theoretical approach. The microscopic model we propose consists of a chain of Majorana Cooper-pair boxes with local tunneling between Majorana zero modes and local charging energy terms, which can be controlled by gate potentials, thus making its realization more feasible.