On asymptotic flatness

Starting with a few basic assumptions on the local asymptotic behavior of space-time and using Penrose's conformal technique the asymptotic behavior of both the physical and unphysical metric is obtained in a Bondi-type coordinate system. The space-times under consideration are not necessarily empty in the asymptotic region nor are they necessarily asymptotically flat. However, they do have the usual falloff behavior as one goes out toward infinity in a given null direction. The assumptions made in this paper and the resultant metrics are compared with those of Persides in his recent paper on the definition of asymptotic flatness.     

On the asymptotic flatness of theC metrics at spatial infinity

It is shown that a family of exact, radiating solutions of Einstein's field equations (theC metrics) is asymptotically flat at spatial infinity (in the sense of Ashtekar-Hansen). The ADM and Bondi masses are discussed.     

Logarithmic Regge pole

This work presents the subtraction procedure and the Regge cut in the logarithmic Regge pole approach. The subtraction mechanism leads to the same asymptotic behavior as previously obtained in the non-subtraction case. The Regge cut, in contrast, introduces a clear role to the non-leading contributions for the asymptotic behavior of the total cross-section. From these results, some simple parameterization is introduced to fit the experimental data for the proton-proton and antiproton-proton total cross-section above some minimum value up to the cosmic-ray. The fit parameters obtained are used to present predictions for the begin{document}$ rho(s)$end{document}-parameter as well as to the elastic slope begin{document}$ B(s)$end{document} at high energies.     

The flatness problem and Lambda

By way of a complete integration of the Friedmann equations, in terms of observables, it is shown that for the cosmological constant Lambda > 0 there exist nonflat Friedmann-Lema?tre-Robertson-Walker models for which the total density parameter omega remains approximately 1 throughout the entire history of the Universe. Further, it is shown that in a precise quantitative sense these models are not finely tuned. When observations are brought to bear on the theory, and, in particular, the Wilkinson microwave anisotropy probe observations, they confirm that we live in just such a universe. The conclusion holds when the classical notion of Lambda is extended to dark energy.     

Logarithmic Quantum Time Crystal

We investigate a time-independent many-boson system, whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit. Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is, T ～ log N. This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit. The logarithmic dependence of i...     

光学平面绝对检验方法的研究

应用两种方法对三个高精度平面进行了测试。第一种方法是Fritz的三面互检法,它利用Zernike多项式的特性拟合三个面四次组合测量得到的干涉图,然后求出三个面的Zernike多项式系数,从而得到三个面的面形偏差。第二种方法是奇偶函数法,根据函数的奇偶性,把平面的面形函数分解为四类:偶奇、奇偶、偶偶和奇奇函数,分别求出各分量,从而得到三个面的三维面形偏差。对两种方法都编制了理论模拟和实测程序,并进行了实验,实现了无参考面的高精度平面面形测试。     

Logarithmic scaling and spontaneous breaking

Indecomposable representations of dilatations allow for logarithms in scale invariant operator product expansion. We prove that in absence of spontaneous breaking, they are incompatible with conformal invariance and positivity.     

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg and lattice vertex algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1) _a , of central charge 1 − 12a ². We classify these operators in terms of depth and provide explicit constructions in all cases. Our intertwining operators resemble puncture operators appearing in quantum Liouville field theory. Furthermore, for a = 0 we focus on the vertex operator subalgebra L(1, 0) of M(1)₀ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of hidden logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1, 0)-module.     

Logarithmic divergence in four-dimensional string theory

Logarithmic divergences in the one-loop scattering amplitude of the heterotic string compactified on the Z_n-orbifold are investigated. The coefficient of these divergences is shown to be a function of the indices of the representations to which the massless states of the model belong.     

Logarithmic hierarchy of universal dielectric response

A hierarchy of logarithmically sequenced relaxation rates establishes a model for the "universal dielectric response", which is widely observed in condensed matter and displays a continually decelerated response in striking contrast to Debye relaxation. The model accounts for the phase shifts between external stimulus and relaxation and leads to the frequency-independent ratio of imaginary to real part of the susceptibility.Permanent address     

Logarithmic islanding in submonolayer epitaxial growth

We investigate submonolayer epitaxial growth with a fixed monomer flux and irreversible aggregation of adatom islands due to an effective island diffusion, with a diffusivity for an mass k island proportional to . For , there is a steady state, while for , continuously evolving logarithmic islanding occurs in which the island density grows extremely slowly, as . In the latter regime, the island size distribution exhibits complex, but universal, multiple-scale mass dependence which we account for theoretically. Received: 3 June 1998 / Accepted: 13 July 1998     

Myerse-Perry Black Holes with Logarithmic Correction

In this paper we consider Myers-Perry black holes and study thermodynamics and statistics under logarithmic correction of the entropy. We calculate effect of logarithmic correction of thermodynamics quantities such as entropy. We study thermodynamics stability of the model by using the specific heat. We claim that the correction term removes some instabilities and matches statistical entropy with BH entropy.     

Logarithmic correlation functions in two-dimensional turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c_8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k^−5.125 ln(k) for perturbed 2D-turbulence and E(k) ∼ k⁻⁵ ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.     

Logarithmic operators in conformal field theory

Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary operators form the basis of the Jordan cell for the operator L₀. An example of the field theory possessing such correlation functions is given.     

Logarithmic correction to BMSFT entanglement entropy

Using Rindler method we derive the logarithmic correction to the entanglement entropy of a two dimensional BMS-invariant field theory (BMSFT). In particular, we present a general formula for extraction of the logarithmic corrections to both the thermal and the entanglement entropies. We also present a CFT formula related to the logarithmic correction of the BTZ inner horizon entropy which results in our formula after taking appropriate limit.