Ordinary Theory Research Articles

N-Dimensional non-commutative GUP quantization and application to the Bianchi I model

We analyse a n-dimensional Generalized Uncertainty Principle (GUP) quantization framework, characterized by a non-commutative nature of the configurational variables. First, we identify a set of states which are maximally localized only along a single direction, at the expense of being less localized in all the other ones. Subsequently, in order to recover information about localization on the whole configuration space, we use the only state of the theory which exhibits maximal localization simultaneously in every direction to construct a satisfactory quasi-position representation, by virtue of a suitable translational operator. The resultant quantum framework is then applied to model the dynamics of the Bianchi I cosmology. The corresponding Wheeler–DeWitt equation is reduced to Schrödinger dynamics for the two anisotropy degrees of freedom, using a WKB representation for the volume-like variable of the Universe, in accordance with the Vilenkin scenario. The main result of our cosmological implementation of the constructed quantum theory demonstrates how the dynamics of a wave packet peaked at some point in the configuration space represented in the quasi-position variables favours as the most probable configuration exactly the initial one for a relatively long time, if compared with the ordinary quantum theory. This preference arises from the different dynamical behavior exhibited by wave packets in the two quantum theories.

The homology digraph of a preordered space

This paper studies a notion of directed homology for preordered spaces, called the homology digraph. We show that the homology digraph is a directed homotopy invariant and establish variants of the main results of ordinary singular homology theory for the homology digraph. In particular, we prove a Künneth formula, which enables one to compute the homology digraph of a product of preordered spaces from the homology digraphs of the components.

The influence functional in open holography: entanglement and Rényi entropies

Open quantum systems are defined as ordinary unitary quantum theories coupled to a set of external degrees of freedom, which are introduced to take on the rôle of an unobserved environment. Here we study examples of open quantum field theories, with the aid of the so-called Feynman-Vernon Influence Functional (“IF”), including field theories that arise in holographic duality. We interpret the system in the presence of an IF as an open effective field theory, able to capture the effect of the unobserved environment. Our main focus is on computing Rényi and entanglement entropies in such systems, whose description from the IF, or “open EFT”, point of view we develop in this paper. The issue of computing the entanglement-Rényi entropies in open quantum systems is surprisingly rich, and we point out how different prescriptions for the IF may be appropriate depending on the application of choice. A striking application of our methods concerns the fine-grained entropy of subsystems when including gravity in the setup, for example when considering the Hawking radiation emitted by black holes. In this case we show that one prescription for the IF leads to answers consistent with unitary evolution, while the other merely reproduces standard EFT results, well known to be inconsistent with unitary global evolution. We establish these results for asymptotically AdS gravity in arbitrary dimensions, and illustrate them with explicit analytical expressions for the IF in the case of matter-coupled JT gravity in two dimensions.

The “Russian bots” between social and technological: Examining the ordinary folk theories of Twitter users

The bots’ activity is already frequently documented in the literature, and the war between Russia and Ukraine accentuated this scholarly interest for users’ sensemaking. Applying folk theories framework on 56 semi-structured interviews with users who tweet about “Russian bots,” I examine how bots might be understood as structural-computational entities, with complex roles in shaping digitally mediated realities. Findings reveal several theories associated with Russian bots. First, participants believe that these bots actively endorse users’ political enemies, which are mainly politicians from the participants’ countries. Second, such bots are considered to increase animosities between users, as participants actively unfollow their peers on Twitter and unfriend them in real life, based on their opinions regarding the war in Ukraine. Third, bots boost users’ digital activity, given the fact that participants consider them responsible for artificially increasing the popularity of certain accounts or, on the contrary, for systematic and aggressive attacks against others.

Cartesian double theories: A double-categorical framework for categorical doctrines

The categorified theories known as “doctrines” specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category theory. A cartesian double theory is defined to be a small double category with finite products and a model of a cartesian double theory to be a finite product-preserving lax functor out of it. Many familiar categorical structures are models of cartesian double theories, including categories, presheaves, monoidal categories, braided and symmetric monoidal categories, 2-groups, multicategories, and cartesian and cocartesian categories. We show that every cartesian double theory has a unital virtual double category of models, with lax maps between models given by cartesian lax natural transformations, bimodules between models given by cartesian modules, and multicells given by multimodulations. In many cases, the virtual double category of models is representable, hence is a genuine double category. Moreover, when restricted to pseudo maps, every cartesian double theory has a virtual equipment of models, hence an equipment of models in the representable case. Compared with 2-monads, double theories have the advantage of being straightforwardly presentable by generators and relations, as we illustrate through a large number of examples.

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Mathematical Modeling of the Transmission Dynamics of Gumboro Disease

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number Rog is derived, and the dynamical behaviors of both the disease‐free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever Rog < 1 and an asymptotic stable EE whenever Rog > 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings.

Non-Abelian Landau-Ginzburg theory of ferromagnetic superconductivity and mixing between U(1) and SU(2) gauge bosons

We propose an effective theory of non-Abelian superconductivity, an SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory, which could be viewed as an effective theory of ferromagnetic superconductivity made of spin-up and spin-down doublet Cooper pair. Just like the Abelian Landau-Ginzburg theory it has the U(1) electromagnetic interaction, but the new ingredient is the non-Abelian SU(2) gauge interaction between the spin doublet Cooper pairs. A remarkable feature of the theory is the mixing between the U(1) gauge boson and the diagonal part of the SU(2) gauge boson. After the mixing it has a massless non-Abelian gauge boson (the massless s-boson) and massive gauge boson (the massive photon), in addition to the massive off-diagonal non-Abelian gauge bosons (the massive s-bosons) which induce the spin-flip interaction between the spin up and down components of the Cooper pair. So, unlike the ordinary Landau-Ginzburg theory it has a long range interaction mediated by the massless s-boson, which could be responsible for the long range magnetic order and spin waves observed in ferromagnetic superconductors. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different penetration lengths, the one fixed by the mass of the photon (which generates the well known Meissner effect) and the other fixed by the mass of the off-diagonal gauge bosons (which determines the range of the spin flip interaction). The non-Abelian structure of the theory naturally accommodates new topological objects, the non-Abrikosov quantized spin vortex (as well as the well known Abrikosov vortex) and non-Abelian spin monopole. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory.

Non-perturbative Lee-Wick gauge theory: Towards Confinement & RGE with strong couplings

We consider a non-Abelian Lee–Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo–Ojima approach, and obtain the functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee–Wick heavy mass scales (M). We show that the fate of the ghosts are fixed in these regimes: they are no more the propagating degrees of freedom in the infrared-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit , one recovers the standard results for the local non-Abelian Yang-Mills theory.

The Born Rule is a Feature of Superposition

The Born Rule plays a critical role in quantum mechanics (QM) since it supplies the link between the mathematical formalism and experimental results in terms of probabilities. The Born Rule does not occur in ordinary probability theory. Where then does it come from? This has been a topic of considerable controversy in the literature. We take the approach of asking what is the simplest extension of ordinary probability theory where the Born rule appears. This is answered by showing that the Born Rule appears by adding the notion of superposition events (in addition to the ordinary discrete events) to finite probability theory. Hence the rule does not need any physics-based derivation. It is simply a feature of the mathematics of superposition when only superposition events are added to ordinary probability theory.

Ordinary state-based peridynamic modelling of crack propagation in functionally graded materials with micro cracks under impact loading

Crack propagation in functionally graded materials containing micro cracks is investigated using ordinary state-based Peridynamic theory. This study focuses on the dynamic fracture behavior of FGMs adapted to the Kalthoff–Winkler experiment. The results demonstrate that as cracks propagate from regions with lower material properties to regions with higher properties and increasing Poisson’s ratio, crack velocities decrease while toughness increases. Furthermore, the direction of crack propagation tends to align with weaker regions as the material properties transition from a zone of low stiffness and low Poisson’s ratio to a zone of high stiffness and high Poisson’s ratio.

A peridynamic model for rail crack initiation with cavity defect

Cavity defects can aggravate the rail crack initiation. To study their effect on rail fatigue crack initiation behaviour, a peridynamic model of rail crack initiation considering the characteristics of the cavity defect was proposed. First, based on the low-cycle fatigue test data, the bond failure criterion of the rail material was derived and verified to characterize the fatigue damage performance. Then, mathematical expressions for circular, triangular and rectangular defect characteristics were proposed, establishing a prefabricated method for rail cavity defects. Based on the ordinary state-based peridynamic fatigue theory, a rail crack initiation model with the cavity defect was constructed. Finally, the behaviour of rail crack initiation with the cavity defect was analysed.

Projective spacetime symmetry of spacetime crystals

Wigner’s seminal work on the Poincaré group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincaré group could be the spacetime groups of periodically driven crystals or spacetime crystals featuring spacetime periodicity. In this study, we establish the general theory of projective spacetime symmetry algebras of spacetime crystals and reveal their intrinsic connections to gauge structures. As important applications, we exhaustively classify (1,1)D projective symmetry algebras and systematically construct spacetime lattice models for them all. Additionally, we present three consequences of projective spacetime symmetry that surpass ordinary theory: the electric Floquet-Bloch theorem, Kramers-like degeneracy of spinless Floquet crystals, and symmetry-enforced crossings in the Hamiltonian spectral flows. Our work provides both theoretical and experimental foundations to explore novel physics protected by projective spacetime symmetry of spacetime crystals.

Scalar QED in AdS

We consider scalar QED with Nf flavors in AdSD. For D < 4 the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large Nf. We then apply this result to compute the boundary four-point function of the charged operators at leading order in 1/Nf and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large Nf, in integer dimension D = 3 an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.

Propeller-Ice Contact modelling with Peridynamics

Ice loads pose a significant threat to ice-class propellers in frozen waters, making it crucial to analyse the magnitude of ice loads. However, the complex mechanical properties of ice and its failure process make it challenging to investigate the correlation between ice-propeller contact phenomena and ice loads. This paper uses a PC3 class propeller blade to study the propeller-ice contact process. This study involves developing ice failure and propeller blade models based on ordinary and non-ordinary state-based peridynamics theory and validating them using experimental. Convergence analysis was performed before blade ice loads evaluation. Additionally, we investigate the effect of the pitch angle on the ice-milling process.

Simulation of Brittle Materials Based on Ordinary State-based Peridynamics

We present a coupled model for brittle materials based on the ordinary state-based peridynamics. The ordinary state-based peridynamics theory is suitable for describing the plastic incompressibility problem and has good application prospects in the fracture damage simulation of brittle materials. The brittle material is a material with a compressive load-bearing capacity greater than the tensile load-bearing capacity and has the characteristics of incompressibility, which is consistent with the application scope of ordinary state-based peridynamics. The mechanical behavior of brittle materials is simulated and analyzed using the ordinary state-based peridynamics theory coupled with brittle materials, and the validity of the model is verified using the finite element method. The results show that the model can effectively capture the displacement field distribution of the brittle material, and the comparison of the finite element results displacement field is consistent. Finally, crack extension analysis is performed on the brittle material plate with prefabricated defects, where the cracks extend along the defect location, bifurcate, and finally penetrate the upper and lower surfaces of the material. The results show that the model can effectively predict the crack expansion path of the material, which provides a new research idea for the simulation of crack expansion in brittle materials.

Kink–antikink interaction forces and bound states in a nonlinear Schrödinger model with quadratic and quartic dispersion

In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schrödinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a “lower branch” adhering to the energy landscape of the 2-kink states. We also, however, study in detail the “upper branches” bearing higher numbers of kinks. In addition to computing the stationary states and analyzing their stability within the partial differential equation model, we develop an effective particle ordinary differential equation theory that is shown to be surprisingly efficient in capturing the kink equilibria and normal (as well as unstable) modes. Finally, the results of the bifurcation analysis are corroborated by means of direct numerical simulations involving the excitation of the states in a targeted way in order to explore their instability-induced dynamics.

General Theory of Momentum-Space Nonsymmorphic Symmetry

As a fundamental concept of all crystals, space groups are partitioned into symmorphic groups and nonsymmorphic groups. Each nonsymmorphic group contains glide reflections or screw rotations with fractional lattice translations, which are absent in symmorphic groups. Although nonsymmorphic groups ubiquitously exist on real-space lattices, on the reciprocal lattices in momentum space, the ordinary theory only allows symmorphic groups. In this work, we develop a novel theory for momentum-space nonsymmorphic space groups ($k$-NSGs), utilizing the projective representations of space groups. The theory is quite general: Given any $k$-NSGs in any dimensions, it can identify the real-space symmorphic space groups ($r$-SSGs) and construct the corresponding projective representation of the $r$-SSG that leads to the $k$-NSG. To demonstrate the broad applicability of our theory, we show these projective representations and therefore all $k$-NSGs can be realized by gauge fluxes over real-space lattices. Our work fundamentally extends the framework of crystal symmetry, and therefore can accordingly extend any theory based on crystal symmetry, for instance, the classification crystalline topological phases.

Thermally driven elastic membranes are quasi-linear across all scales

We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating a model known as the overdamped dynamic Föppl–von Kármán equation, in which the Föppl–von Kármán equation from elasticity theory is driven by white noise. The resulting nonlinear equation is governed by a single nondimensional coupling parameter g where large and small values of g correspond to weak and strong nonlinear coupling respectively. By analysing the weak coupling case with ordinary perturbation theory and the strong coupling case with a self-consistent methodology known as the self-consistent expansion, precise analytic predictions for the static and dynamic structure factors are obtained. Importantly, the maximum frequency supported by the system plays a role in determining which of three possible classes such sheets belong to: (1) when , the system is mostly linear with roughness exponent ζ = 1 and dynamic exponent z = 4, (2) when , the system is extremely nonlinear with roughness exponent and dynamic exponent z = 3, (3) between these regimes, an intermediate behaviour is obtained in which a crossover occurs such that the nonlinear behaviour is observed for small frequencies while the linear behaviour is observed for large frequencies, and thus the large frequency linear tail is found to have a significant impact on the small frequency behaviour of the sheet. Back-of-the-envelope calculations suggest that ultra-thin materials such as graphene lie in this intermediate regime. Despite the existence of these three distinct behaviours, the decay rate of the dynamic structure factor is related to the static structure factor as if the system were completely linear. This quasi-linearity occurs regardless of the size of g and at all length scales. Numerical simulations confirm the existence of the three classes of behaviour and the quasi-linearity of all classes.

2D numerical modeling of solid materials with virtual boundary particles in ordinary state-based peridynamics

The peridynamic method has become an important theory for predicting crack propagation in solid materials, but due to its non-locality, the boundary material particles will affect the accuracy of the simulation results. For some specimens without a notch or small notch, it is even impossible to simulate the correct path of crack propagation. Therefore, based on the ordinary state-based peridynamic theory, this paper proposes a virtual boundary particles method for simulating solid materials and gives the force formula of virtual particles. The accuracy and precision of the results are improved by arranging virtual particles on the boundary of the model. For quasi-static problems, the simulation results show that the model with virtual boundary particles has higher accuracy. The three-point bending simulation of the long-notch specimen shows that the virtual boundary particles method can reduce the influence of boundary particles on the simulation results. Then, three-point bending simulations are performed on unnotched and small-notched specimens, and the results show that the model with virtual boundary particles could accurately predict crack propagation direction and is more consistent with the experimental results, which verify the validity of the model.