Phase change on transmission of microwaves through metal disc delay dielectrics

Expressions for the phase changeΦ suffered by microwaves when transmitted through an artificial dielectric composed of metallic discs arranged in a three-dimensional array have been derived with different approaches as follows (i) molecular theory, (ii) electromagnetic theory and (iii) transmission line theory. The phase change depends on the distancet that the wave traverses inside the dielectric and also the spacingd between centre to centre of any two adjacent discs in the three principal directions. Molecular theory indicatesΦ as an increasing function oft, whereas, the other two theories indicateΦ as an oscillatory function oft. The transmission line theory also exhibitsΦ to be real or imaginary depending ont. Experimental values ofΦ as a function oft have been obtained with the help of a microwave (3·2 cms wavelength) interferometer for two dielectrics havingd as 1·91 cms and 2·22 cms respectively.     

The Hilbert series of the one instanton moduli space

The moduli space of k G-instantons on \( {\mathbb{R}^4} \) for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have \( \mathcal{N} = 2 \) supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.     

Boundary Conditions for Topological Quantum Field Theories,Anomalies and Projective Modular Functors

We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level m, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for n-characters on ∞-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for n + 1-dimensional TQFTs produce n-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Winkelverteilungen elastisch an Edelgas-Atomstrahlen gestreuter Elektronen; Spinpolarisation eines an Argon gestreuten 40 eV-Elektronenstrahls

Various non-leptonic decay modes of baryons are calculated in a simple quark model. Form factors for various matrix elements are taken both from experiment and the quark model. Additionally theK→2π andK→3π decay modes are computed in the same model. The theory has theΔ I=1/2 rule and static SU⁶ built-in. A relation between the∑ ⁺→N ⁺ π ⁺ decay, not calculable in the model, and theK→3π decay is given via an effective six quark interaction. Agreement with experiment is order of magnitude for the baryonic decays and worse for theK decays.     

Horizon thermodynamics in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) theory

We investigate whether the new horizon first law proposed recently still work in f(R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in f(R) theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in f(R) theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Characteristic features of the singlet–triplet mechanism of the electron spin polarization

Characteristic features of net chemically induced dynamic electron spin polarization (CIDEP) P _n in triplet–radical (TR) quenching are analyzed in detail within the framework of a general model that enables one to analyze CIDEP both numerically and analytically. This model also makes it possible to accurately describe the nonadiabatic transitions between the terms of the TR-pair spin Hamiltonian that lead to CIDEP generation. The proposed theory yields a simple analytical dependence of P _n on the parameters of the model. In particular, it is shown that, within a wide region of parameters, the dependence of P _n on the coefficient of relative TR diffusion D _r is described by a simple linear relation: \(P_n^{ - 1}\left( {{D_r}} \right) = {Q_0} + \overline {{q_n}} {D_r}\) (with Q ₀ and \({{q_n}}\) independent of D _r ). It is also demonstrated that the numerical and analytical results obtained are very useful in analysis of experimental data, as demonstrated by analyzing the experimental dependence of P _n on D _r .     

Higher order corrections to the Lipatov asymptotics in the ϕ<Superscript>4</Superscript> theory

Higher orders in perturbation theory can be calculated by the Lipatov method [1]. For most field theories, the Lipatov asymptotics has the functional form ca ^N Γ(N+b (N is the perturbation theory order); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of higher order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the field theory in question. These coefficients are calculated quantitatively for the n-component ?⁴ theory under the assumption that the second instanton is (i) a combination of elementary instantons and (ii) a spherically asymmetric localized function. A technique of two-instanton computations, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state, is developed.     

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.     

An investigation of ab initio shell-model interactions derived by no-core shell model

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo’s first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green’s function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.     

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.     

Die kritischen Felder von supraleitenden Indium-Blei-Legierungen

Resistance and magnetization measurements have been made onα-phase Indium Lead alloys in a longitudinal magnetic field. The results have been analyzed in terms of the Ginzburg-Landau-Abrikosov-Gorkov theory and the parameter? of the alloys has been determined. Alloys with concentrations greater than 4.2 at % Pb are superconductors of the second kind. The temperature variation of? depends on the mean free path and is somewhat less pronounced for the more dilute alloys. This behaviour is not adequately described by the recent theories. The phenomena of surface superconductivity and its critical fieldH _c3 are in good agreement with the theory ofSaint-James andde Gennes except for the constantC ₀=H _c3/H _c2 which for all the alloys studied is about 10% higher than the theoretical value 1.694. Electrolytic deposition of Cu on the surface reducesH _c3 and givesC _cu=1.15 and excludes the alternative explanation of surface filaments. The concentration dependences ofT _c andγ show irregularities at 7 at % Pb. They can be explained by the touching of the Fermi surface with the Brillouin zone boundary.     

Violation of causality in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, \(m^2\), defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (\(m^2 < 0\) and \(m=0\)) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads \(h_A^{~\mu }\) up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f(T) gravity does not preclude non-local violation of causality in the form of closed time-like curves.     

Investigation of the critical behavior of the three-dimensional weakly diluted Potts model

The static critical behavior of the three-dimensional weakly diluted Potts model with the state q = 3 on a simple cubic lattice has been investigated by the Monte Carlo method using the Wolff single-cluster algorithm. It is shown that at the spin concentrations p = 0.9 and 0.8 a second-order phase transition is observed in the three-dimensional weakly diluted Potts model with the state q = 3. On the basis of the finite-size scaling theory, we calculated the static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the correlation-length exponent v.     

Thermally activated flux flow,vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca_(0.8)La_(0.2)Fe_(0.98)Co_(0.02)As_2single crystal,a newly discovered 112-type iron pnictide superconductor,are comprehensively studied by magneto-resistivity measurement.The field-dependent activation energy,U_0,is derived in the framework of thermally activated flux flow(TAFF)theory,yielding a power law dependence U_0～H~αwith a crossover at a magnetic field around 2 T in both H⊥ab and H//ab,which is ascribed to the different pinning mechanisms.Moreover,we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model,and vortex phase diagrams are constructed for both H⊥ab and H//ab.Finally,the results of mixed-state Hall effect show that no sign reversal of transverse resistivityρ_(xy)(H)is detected,indicating that the Hall component arising from the vortex flow is in theories or experiments previously reported on some high-T_ccuprates.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

Interferometric Computation Beyond Quantum Theory

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.