Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When , spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.     

Bianchi-I Universe with Decaying Vacuum Energy Density and Time Varying Gravitational Constant

Anisotropic Locally Rotationally Symmetric Bianchi-I (LRSBI) cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Our calculations for the Supernova constraints concerning the luminosity distance provide reasonable results.     

Eleven Spherically Symmetric Constant Density Solutions with Cosmological Constant

Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.     

Quantum de Sitter Spacetime and Energy Density Contributed from the Cosmological Constant

Previously we introduce a new way to quantize the static SchwarzschiM black hole （SSBH）, there the SSBH was first treated as a single periodic Euclidean system and then the Bohr-Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole [Chin. Phys. Lett. （2004） 21 1887]. Here we try to extend the above method to quantize the static de Sitter （SDS） spacetime and establish a quantum theory of both SDS spaze and the energy density contributed from the cosmological constant.     

The Mode Solution of the Wave Equation in Kasner Spacetimes and Redshift

We study the mode solution to the Cauchy problem of the scalar wave equation □φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift.     

Spatial Random Permutations and Infinite Cycles

We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.     

Covariant Sectors with Infinite Dimension¶and Positivity of the Energy

Let ? be a local conformal net of von Neumann algebras on S ¹ and ρ a M?bius covariant representation of ?, possibly with infinite dimension. If ρ has finite index, ρ has automatically positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but, as seen by an example, it may contain negative values. We then consider nets with Haag duality on ℝ, or equivalently sectors with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely this is the case iff there exists an unbounded M?bius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition. Received: 21 April 1997 / Accepted: 23 September 1997     

Constant Term Solution for an Arbitrary Number of Osculating Lattice Paths

Osculating paths are sets of directed lattice paths which are not allowed to cross each other or have common edges, but are allowed to have common vertices. In this work we derive a constant term formula for the number of such lattice paths by solving a set of simultaneous difference equations.     

Semi-Dispersing Billiards with an Infinite Cusp I

 Let be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f. Under certain conditions on f, we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section corresponding to collisions with the dispersing part of the boundary. The relevant invariant measure for this Poincaré section is infinite, whence the need to surpass the existing results, designed for finite-measure dynamical systems. Received: 1 May 2002 / Accepted: 13 May 2002 Published online: 22 August 2002     

Polaronic Effects on the Impurity Binding Energy in a Polar Crystal Slab Within an Electric Field

The effects of the interaction between electron and bulk longitudinal optical (LO) phonon and surface optical (SO) phonon on the impurity binding energy of the ground state in a polar crystal slab within an external electric field are derived by using the method of a variational wavefunction. The binding energy of the bound polaron is obtained as a function of the impurity position, the slab thickness and the electric field strength. It is found that the polaronic correction to the impurity binding energy by the SO phonon may be enhanced and that by the LO phonon may be reduced with increasing electric field strength. And the effect of the electron-phonon interaction is quite important in increasing the values of binding energy.     

Pressure-Driven Ne-Bearing Polynitrides with Ultrahigh Energy Density

Neon（Ne） can reveal the evolution of planets,and nitrogen（N） is the most abundant element in the Earth’s atmosphere.Considering the inertness of neon,whether nitrogen and neon can react has aroused great interest in condensed matter physics and space science.Here,we identify three new Ne-N compounds(i.e.,NeN₆,NeN₁₀,and NeN₂₂) under pressure by first-principles calculations.We find that inserting Ne into N₂ substantially decreases the polymeric pressure...     

Calculation of the Screening Constant and Energy of a Two-Electron Atom

Russian Physics Journal - Using the results of a paper previously published by the author, general expressions have been obtained for the energy and screening constant for a two-electron atom for...     

Density of Energy Spectrum of an Electron in the Image-Potential Field and a Trapping Electric Field

Optics and Spectroscopy - Density of energy spectrum of an electron bound by an image-potential field and a trapping field near the surface of a metal is calculated in the quasi-classical...     

Spectral Energy Density in a Kerr Nonlinear Blackbody

In a Kerr nonlinear blackbody, bare photons with opposite wave vectors and helicities are bound into pairsand unpaired photons are transformed into a new kind of quasiparticle, the nonpolariton. The nonpolariton system constitutes free thermal radiation in the blackbody. The present paper investigates the spectral energy density of the thermal radiation. It is found that the spectral energy density of a Kerr nonlinear blackbody is larger than that of a normal blackbody.     

Spectral Energy Density in a Kerr Nonlinear Blackbody

In a Kerr nonlinear blackbody, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into a new kind of quasiparticle, the nonpolariton. The nonpolariton system constitutes free thermal radiation in the blackbody. The present paper investigates the spectral energy density of the thermal radiation. It is found that the spectral energy density of a Kerr nonlinear blackbody is larger than that of a normal blackbody.     

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.     

密度和温度相关的对称能

利用Hartree–Fock理论,基于扩展的Skyrme有效相互作用,在抛物线近似下,解析地给出了零温度时对称能的密度相关形式.同时讨论了对称能的温度相关性,发现对称能随着温度的升高而减小,在温度较低时,对称能强度系数与温度的关系能较好地符合抛物线规律.