Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories and cosmology, many models contain more than just one scalar field (e.g., inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form, and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g., dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g., spherically reduced scalar-tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.     

$\mathfrak{D}$-Differentiation in Hilbert Space and the Structure of Quantum Mechanics Part II: Accelerated Observers and Fictitious Forces

We investigate a possible form of Schrödinger’s equation as it appears to moving observers. It is shown that, in this framework, accelerated motion requires fictitious potentials to be added to the original equation. The gauge invariance of the formulation is established. The example of accelerated Euclidean transformations is treated explicitly, which contain Galilean transformations as special cases. The relationship between an acceleration and a gravitational field is found to be compatible with the picture of the ‘Einstein elevator’. The physical effects of an acceleration are illustrated by the problem of the uniformly-accelerated harmonic oscillator.     

On the energy of formation of defects

We present a formulation of the Gibbs free energy of defect formation in crystals which is formally based on a quasi-classical thermodynamical cluster expansion of the Gibbs free energy of the defect crystal. Thus a microscopic formulation of the Gibbs free energy of formation is achieved. The related quantities like formation volume per defect and defect susceptibility functions are then derived from the formation energy. The resulting expressions depend only on the defect concentration and the bulk properties of the crystal. Finally we discuss an approximate form of the formation energy which was introduced intuitively by Varotsos and Alexopoulos. As an example for the applicability of this formulation we present an explanation of the anomaly in the conductivity and diffusion of AgBr.     

Superspace unmasked: The physical interpretation of supergravity theory

Supergravity admits a geometric formulation in terms of an expanded algebra of functions on ordinary spacetime. This formulation, called graded manifold theory, is equivalent to the usual superspace supergravity constructions but avoids the anticommuting coordinates of superspace. The geometry suggests an operational interpretation of supergravity theory in terms of measurements made by local observers in spacetime.     

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.     

Naked Singularity of the Vaidya-de Sitter Spacetime and Cosmic Censorship Conjecture

We investigate the formation of a locally nakedsingularity in the collapse of radiation shells in anexpanding Vaidya-de Sitter background. This is achievedby considering the behaviour of non-spacelikeand radial geodesics originating at thesingularity. A specific condition is determined for theexistence of radially outgoing, null geodesicsoriginating at the singularity which, when thiscondition is satisfied, becomes locally naked. Thiscondition turns out to be the same as that in thecollapse of radiation shells in an asymptotically flatbackground. Therefore we have established, at least forthe case considered here, that the asymptoticflatness of the spacetime is not essential for thedevelopment of a locally naked singularity. Our resultthen unequivocally supports the view that no specialrole be given to asymptotic observers (or, for thatmatter, any set of observers) in the formulation of theCosmic Censorship Hypothesis.     

Linking covariant and canonical general relativity via local observers

Hamiltonian gravity, relying on arbitrary choices of ‘space,’ can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between ‘spatial’ and ‘temporal’ variables. The key is viewing dynamical fields from the perspective of a field of observers—a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the ‘space of observers’ is fundamental, and spacetime geometry itself may be observer-dependent.     

Quantum geometry from coordinate transformations relating quantum observers

The relativity principle that the law of propagation for light has the same form for all macroscopic observers is extended to include quantum observers; i.e., observers who may be large, but not infinitely large, by comparison with quantum mechanical systems. This leads to the extension of the covariance group from the diffeomorphisms to the conservation group (which is the largest group of coordinate transformations under which conservation laws are covariant statements) and, thus, to the quantum geometry and quantum unified field theory considered in a previous paper.     

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically, we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy?Cmomentum tensor of the source is analyzed.     

Dead time corrections to photon counting statistics II: Quantum theory

The recent formulation of the quantum theory of photodetection, based on the quantum theory of continuous measurements, is extended to the case of a (nonideal) detector which has non-zero dead time. A general result is proven which expresses the dead time modified counting statistics in terms of the counting statistics of anassociated ideal detector. As an illustration, the dead time corrections to the counting statistics of a single-mode free field are worked out, and these corrections are shown to be identical in form to the dead time corrections for a classical optical field of constant intensity.     

Nonlinear optical response in gapped graphene

We present a formulation for the nonlinear optical response in gapped graphene, where the low-energy single-particle spectrum is modeled by massive Dirac theory. As a representative example of the formulation presented here, we obtain a closed form formula for the third harmonic generation in gapped graphene. It turns out that the covariant form of the low-energy theory gives rise to peculiar logarithmic singularities in the nonlinear optical spectra. The universal functional dependence of the response function on dimensionless quantities indicates that the optical nonlinearity can be largely enhanced by tuning the gap to smaller values.     

On defining the spin moment in the tetrad theory of gravitation

A general definition of the spin moment is presented in the tetrad formulation of the relativistic theory of gravitation; it is based on the conditions for the invariance of the corresponding action integral relative to infinitesimal tetrad transformations (the so-called tetrad spin moment) and infinitesimal coordinate transformations (the so-called coordinate spin moment). It is shown that the tetrad formulation of the general theory of relativity (TFGTR) and the tetrad theory of gravitation (TTG) in a space of absolute parallelism lead to fundamentally different definitions of spin, since in the Riemannian geometry of the TFGTR only the coordinate spin moment is physically meaningful, whereas in the space of absolute parallelism of the TTG only the tetrad spin moment has essential significance. It is also indicated that the Pellegrini-Plebanski theory (PPT) leads to an unsatisfactory hybrid definition of spin in the form of the coordinate spin moment of the gravitational and boson fields and the tetrad spin moment of the gravitational and fermion fields, the gravitational field entering into these spin moments of the PPT with opposite signs.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 68–71, May, 1976.     

热漫散射贡献的高能电子衍射吸收结构因子的Doyle-Turner解析表述

给出了一种数值计算高能电子衍射吸收结构因子的方法,并利用模拟退火结合保温相变以及线性最小二乘拟合等算法,对所计算出的吸收结构因子数值进行了含10个参数的Doyle-Turner解析表述的拟合,作为示例,给出Be,AlAs,Ag,Au等5个元素的拟合结果和精度,并作出Al的绝对偏差量和相对偏差量曲线     

Lorentz Covariant Canonical Formalism for Free Massive, Massless and Tachyonic Particles

We construct a consistent Lorentz-covariant canonical formalism for a free massive, massless and tachyonic particle in the framework of the absolute synchronization scheme of clocks. In the case of a massive particle our approach is canonically equivalent to the standard formulation which is not manifestly covariant. The absolute synchronization scheme seems to be the only one we can apply in the case of massless and tachyonic particles.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

Quantification of Gloss Perception as a Function of Stimulus Duration

The mechanism and temporal characteristics of gloss perception are not entirely clear. In addition, the formulation for predicting gloss perception from photometric values has not been established. In the present study, we conducted an experiment to measure several temporal characteristics of gloss perception in order to clarify the mechanism. All stimuli were rendered as computer graphics with Phong and Lambert models to provide gloss perception to human observers. We measured perceptual glossiness with a magnitude estimation method and perceptual diffuse/specular reflectance of test stimuli with a matching method under several stimulus conditions, such as reflectance coefficients and stimulus duration. The results showed that the perceptual specular component and perceptual glossiness increase with decreasing stimulus duration. Finally, we proposed a formulation to predict perceptual glossiness as a function of stimulus duration.