Dynamic of Scalar Bosons in Aharonov-Bohm Magnetic Field

We study the dynamic of scalar bosons in the presence of Aharonov-Bohm magnetic field. First, we give the differential equation that governs this dynamic. Secondly, we use variational techniques to show that the following Schrödinger-Newton equation: , where A is an Aharonov-Bohm magnetic potential, has a unique ground-state solution.

Real scalar field scattering in the nearly extremal Schwarzschild de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter （SdS） space. The approximations naturally lead to the invertible x（r） and the global replacement of the true potential by a PSshl-Teller one. Meanwhile, the Schr6dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate τ.

Real scalar field scattering with polynomial approximation around Schwarzschild–de Sitter black-hole

As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.

Effects of Interaction Between Gravitation and Nonlinear Electrodynamics On Scalar Field Evolution

在这份报纸，我们由使用第三顺序的 WKB 近似在 dyadosphere spacetime 调查分级的地进化。我们发现在引力和非线性的 electrodynamics 之间的联合术语让分级的地更快速腐烂，它也让分级的地更慢慢地震荡。在另外的词上，这个联合术语作为一个抑制因素在分级的地进化上生效。同时，这些效果与更高的角度量数字为分级的地变得更明显。

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm （AB） flux fields on the energy levels of a two-dimensional （2D） Klein Gordon （KG） particle subjected to an equal scalar and vector pseudo-harmonic oscillator （PHO）. We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential param- eter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov Uvarov （NU） method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

GFFD： Generalized free-form deformation with scalar fields

The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.

Exact Static Plane Symmetric Soliton-Like Solutions to the Nonlinear Interacting Electromagnetic and Scalar Field Equations in General Relativity

This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the interaction of fields between two different elementary particles by expressing their physical properties. For that, we have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function P(I). It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density. Moreover, the total charge of particles is finite and the total energy of the interaction fields is bounded. It have been emphasized the importance to the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions. In flat space-time, soliton-like solutions exist but the total energy of the interaction fields is equal to zero. We have also shown that in the linear case, soliton-like solutions are absent.

Resonant frequencies of massless scalar field in rotating black-brane spacetime

This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.

STUDY OF EXPLICIT ANALYTIC SOLUTIONS FOR THE NONLINEAR COUPLED SCALAR FIELD EQUATIONS

By using two different transformations, several types of exact analytic solutions for a class of nonlinear coupled scalar field equation are obtained, which contain soliton solutions, singular solitary wave solutions and triangle function solutions. These results can be applied to other nonlinear equations. In addition, parts of conclusions in some references are corrected.

A comparison of phantom linear scalar field and non-linear Born-Infeld scalar field

This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.

Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole （LQBH）using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner-NordstrSm black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.

Brief Note on a Scalar Quantum Field with Finite Lifetime in a Lorentz Invariant Non-Rectangular Euclidean Space

A not necessary rectangular Euclidean space (NoNRES) is constructed, in which one obtains a generally Lorentz invariant scalar product for the low energy sector (LES). This sector is defined for energies below the Planckian limit. If the energy is zero, the NoNRES becomes rectangular and due to the Lorentz invariance, it is applicable for the complete LES of the theory. In contrast to the usual Minkowski space the metric of the NoNRES depends on the kinetic energy of the observed quantum particles. It is assumed that this metric may be useful to derive the scattering cross-section of the corresponding quantum field theory. This assumption is related to the occurrence of divergent loop momentum integrals caused by including the infinite energy range above the Planckian limit (high energy sector or HES). Due to its energy dependence, the metric in both energy sectors differs. In the HES, it depends on the effective dimension of the NoNRES. This dependency results from fluctuations of the space-time above the Planckian limit. Even if they are not part of the theory (as they would be in quantum gravity), these fluctuations should not be ignored. The effective dimension decreases if the energy of the considered particle increases. Since this is true for the HES only, the ultraviolet divergences of loop integrals seem to vanish without distorting the results of the LES. The mechanism is illustrated by calculating the tadpole integral occurring for a simple self-interacting scalar quantum field (with the Higgs mass as example). One obtains a finite contribution for the integral and consequently for the lifetime of the scalar particle.

Noise-Induced Origin of the Fundamental Scalar Field

The physical nature of the fundamental scalar field generation and hence the origination of the Universe is a matter of the discussions for many years. We propose to use the statistical approach to the description of the steady states of the quasi stationary systems with the elements of the quantum field theory methods as a basis to explain the appearance of the cosmological scalar field. Particularly, we apply two fundamental principles, i.e., the H-theorem and least-energy principle to show principal possibility of the scalar field origination. Along with the basic statement that in the presence of the fundamental scalar field, the energy of the vacuum ground state is lower than the ground state energy of the vacuum with no scalar field (primary vacuum), and with regard to the nonlinear interaction of fluctuating physical fields with the scalar field, these principles are employed to reveal probable phase transitions that may be associated with origin and further evolution of the Universe. Thus, we propose the possible physical justification of the spontaneous cosmological scalar field generation.

Examining a Fifth Force Application by Using Dilaton Model and Padmanabhan Inflaton Scalar Field in Early Universe to Generate GW and Gravitons

On page 17 of a book on Modified Gravity by Li and Koyama, there is a discussion of how to obtain a Fifth force by an allegedly non-relativistic approximation with a force proportional to minus the spatial derivative of a scalar field. If the scalar field says for an inflaton, as presented by Padmanabhan only depends upon time, of course, this means that no scalar field contributing to a fifth force our proposal in the neighborhood of Planck time is to turn the time into being equal to r/[constant times c]. This is in the neighborhood of Planck time. Then having done that, consider the initially Plank regime inflaton field as being spatially varying and from there apply a fifth force as a way to help initiate black hole production and possibly Gravitons.

Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in(1+1)-Dimensional Spacetime

有混血儿(Dirichlet Neumann ) 的巨大的分级的地的 Casimir 精力边界状况被计算。以便调整模型，作为模式求和方法说出的典型方法和格林的功能方法分别地被使用。调整零点的精力密度取决于分级的域的团，这被发现。当这块地少些是集体的时，结果与以前的文学一致。

Hawking Radiation from Spherically Symmetrical Gravitational Collapse to an Extremal R-N Black Hole for a Charged Scalar Field

Si-Jie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expected number of particles in any wave packet belonging to Hout spontaneously produced from the state |O)in, which confirms the traditional belief that extremal black holes do not radiate particles. Making some modifications, we demonstrate that the analysis can go through for a charged scalar field.

Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-Flat SdS Black String Space with Polynomial Approximation

As one exact candidate of the higher dimensional black hole,the 5D Ricci-flat Schwarzschild-de Sitterblack string space presents something interesting.In this paper,we give a numerical solution to the real scalar fieldaround the Nariai black hole by the polynomial approximation.Unlike the previous tangent approximation,this fittingfunction makes a perfect match in the leading intermediate region and gives a good description near both the eventand the cosmological horizons.We can read from our results that the wave is close to a harmonic one with the tortoisecoordinate.Furthermore,with the actual radial coordinate the waves pile up almost equally near the both horizons.

Novel Localized Excitations of Nonlinear Coupled Scalar Fields

印射非线性的联合分级的领域和著名 4 模型的关系的某扩大答案被介绍。同时，由最近 Jia，黄和 Lou 建议的著名 4 模型的新解决方案启发了，非线性的联合数量的五种新局部性的刺激回答(NCSF ) 系统被获得。

Soliton-Like Spherical Symmetric Solutions to the Electromagnetic and Scalar Nonlinear Induction Field Equations in the General Relativity Theory

In this paper, we have used the static spherical symmetric metric. The parameter of the nonlinearity fields is included in the arbitrary function characterizing the interaction between the electromagnetic and scalar fields. Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric solutions to the electromagnetic and scalar field equations of nonlinear induction. Considering all forms of the solution of Liouville equation, we proved that the metric functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of the elementary particles has a finite value (soliton-like). In the flat space-time, soliton-like solutions exist.

A Unified Definition of Electrostatic and Magnetic Fields

This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.