Gravitating global monopoles in extra dimensions and the braneworld concept

Multidimensional configurations with a Minkowski external spacetime and a spherically symmetric global monopole in extra dimensions are discussed in the context of the braneworld concept. The monopole is formed with a hedgehoglike set of scalar fields φⁱ with a symmetry-breaking potential V depending on the magnitude φ² = φⁱφⁱ. All possible kinds of globally regular configurations are singled out without specifying the shape of V(φ). These variants are governed by the maximum value φ_m of the scalar field, characterizing the energy scale of symmetry breaking. If φ_m < φ_cr (where φ_cr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii, whereas in the “strong field regime,” when φ_m ≥ φ_cr, the monopole may end with a finite-radius cylinder or have two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.     

New measurements of the radiative decay modes of the φ-meson

The radiative decay models of the φ-meson have been studied: e⁺e^?→φ→ηγ→3γ; e⁺e^?→φ→π^oγ→3γ. Cross sections σ_{φ→ηγ→3γ} and σ_{φ→π^oγ→3γ} have been measured at five energies in the φ-meson energy region and clearly show the φ-resonance in the ηγ → 3γ mode as well as in the π^oγ → 3γ mode. From a Breit-Wigner fit to the experimental data the values of the branching ratios are deduced: B_φ→ηγ = (1.5 ± 0.4) × 10^?2; B_φ→π^oγ = (1.4 ± 0.5) × 10^?3.     

2-manifolds of constant curvature, 3-parameter isometry groups and bäcklund transformations

The relationship between the Sine Gordon equation and Riemannian 2-manifolds of constant negative curvature is well known. We point out that it gives rise (locally) to a transitive action of the 3-parameter group SL(2,R) on the manifold. This enables us to elucidate group theoretically the geometry underlying the Bäcklund transformation. The transformation arises by passing from the 2-manifold, a homogeneous space, to 2-submanifolds of SL(2,R) defined by orbits of the solvable subgroup of SL(2,R). A similar approach allows us several other such transformations, for example, transformations linking φ_xx+φ_yy = sinhφ to φ_xx+φ_yy = sinφ and φ_xx+φ_yy = e^2φ to φ_xx+φ_yy = 0.     

作用表示波动方程中与面有关项

这篇短文的内容是:(i)对於量子场论中的i(δψ[σ])/(δσ(x))=V(x,σ)ψ[σ] 如何由寻常的“曲面上的薛定谔方程”导出,作一个较严格的讨论,以及 (ii)讨论上式中的V(x,σ)在什么条件下不包含有σ。我们证明了所需的条件是 (?L^I)/(?φ_μ) (?L^I)/(?φ_ν)=(?²L)/(?φ_μ?φ_ν)F(φ,φ_ρ),式中L,L^I代表总拉格朗日及作用拉格朗日,φ代表场量,φ_μ代表φ/x^μ,F(φ,φ_ρ)代表φ及φ_μ的一个任意函数。     

Theoretical evaluation of the effective work functions for positive-ionic and electronic emissions from polycrystalline metal surfaces

Effective work functions (φ⁺ and φ^e) for positive-ionic and electronic emissions from polycrystalline metals of Nb, Mo, Ta, W and Ir are calculated according to our theoretical model by using those published data on both fractional surface area (F_i) and local work function (φ_i) of each metal surface composed of several patchy faces (1, 2, …, i). Comparison between the theoretical values thus obtained and those experimental data published to date yields the conclusions as follows. (1) With a slight error of less than ∼0.1 eV, the value of φ^e calculated with each of the metals is in fair or good agreement with that determined by experiment. (2) Such agreement is found also with φ⁺ for W. (3) In a typical case of W, where the degree of monocrystallization (δ_m) corresponding to the largest among the values of F_i is less than ∼0.5, the thermionic contrast (Δφ* ≡ φ⁺ − φ^e) is found again to be nearly equal to both theoretical and experimental values reported previously. (4) Each of the five metals shows that Δφ* at δ_m = 0.68-0.95 is smaller than Δφ* at δ_m < 0.5. (5) This result strongly supports our theoretical prediction that Δφ* decreases gradually to zero as δ_m increases beyond ∼0.5 up to ∼1. (6) Particularly, such a surface which has δ_m ≥ 0.96 exhibits Δφ* ≈ 0, apparently equivalent to the so-called “monocrystalline surface (δ_m = 1)”. These results lead to the conclusion that our theoretical model is valid for evaluating the effective work functions probably with a slight error of less than ∼0.1 eV, irrespective of both the surface species and the range of δ_m. In addition, our simple model makes it possible to analyze the mechanism of change in φ⁺ and φ^e according to the change in surface characters of both φ_i and F_i.     

The evaluation of the branching ratios of the decays φ(1020)→2π<Superscript>+</Superscript>2π<Superscript>−</Superscript>π<Superscript>0</Superscript>, π<Superscript>+</Superscript>π<Superscript>−</Superscript>3π<Superscript>0</Superscript>

Combining the Okubo-Zweig-Iizuka rule in the decay φ→ρπ→π⁺π^?π⁰ with the ρ→4π decay amplitudes, we calculate the φ→2π⁺2π^?π⁰ and φ→π⁺π^?3π⁰ ones. The partial widths of the above φ decays are evaluated, and the excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B_φ→π⁺_π^?_3π⁰ ≈ 2 × 10^?7 and B_φ→2π⁺_2π^?_π⁰ ≈ 7 × 10^?7 are such that, with the luminosity L=500 pb^?1 attained at DAΦNE φ factory, one may already possess about 1685 events of the decays φ→5π.     

从X射线的衍射强度测定晶体的德拜特征温度

本文详尽地讨论了从X射线衍射强度测定均匀的且各向同性的晶体的德拜特征温度的方法。本方法指明:如将所有的计算强度对观察强度之比的自然对数In(I_calc/I_obs)对sin²θ/λ²标绘,则应该得到一条直线,这条直线的斜率为2B。在德拜的比热理论中,B可表示为(6h²T/MkΘ_D²){φ(x)+(x/4)},其中x=Θ_D/T。如使G=BMkT/6h²,则φ(x)+x/4=Gx²,既然已求得了B值,则这个方程式中的G是一个可量度的数。求解这个方程式可用图解法来进行。使y₁=Gx²,而y₂=φ(x)+x/4,则从这两个方程式的标绘可以得到两条曲线,这两条曲线的交点就是所要测定的x值,由x值可确定在测定温度时的特征温度。必须指出,由于Θ_D本身是温度的一个函数,本方法提供了一个在所需要的温度测定德拜特征温度的可能性。 关键词：     

Central limit theorem in quantum field theory,generalized partons and application to deep-inelastic scattering

We prove the following elementary theorem. Ifφ ¹,...,φ ^N is a sequence of fields having identical, thougharbitrary, interactions but not interacting with each other and 〈φ _n 〉0,i=1,...,N then the generating functional of the «average» field φ^(N) may be explicitly obtained and may be written in terms of the two-point function of any of the fields φ _i . The theorem is then applied to define generalized parton fields \(\psi _j = \sum\limits_{i = 1}^N {\psi _{ij} } /\sqrt N \) as «averages» of basic fieldsψ _ij havingarbitrary interactions but not interacting with each other. We show that in the limitN→∞ Bjorken scaling, as observed at energies not too high, may be obtained if only quanta associated with generalized parton fields are excited in the hadron by the virtual photonwith no reference to the details of the underlying dynamics. ForN<∞, and the excitation of other quanta as well lead to a systematic breaking of scale invariance and the details of the dynamics are necessarily recovered which are expected to be applicable at higher energy regimes.     

Mass generation in the O(3) non-linear σ model

We study the two-point function of the azimuthal angle, G^(φ)(x) = 〈e^iφ(x)e^?iφ(0)〉_inst [φ = arg (q¹ + iq²), where q^a is a three-component unit vector field], in the dense instanton gas approximation for the two-dimensional O(3) non-linear σ model. We find that G^(φ) (x) decreases exponentially as |x| → ∞. This suggests that the dense instanton gas may generate a mass gap in the O(3) non-linear σ model. The physical mechanism of this mass generation is also discussed.     

Narrow beam emission of slow positrons from negative affinity surfaces

We have measured the angular distribution of the slow positrons (e⁺·) from negative work function (φ⁺) surfaces of Cu and Al bombarded by keV e⁺ in ultrahigh vacuum. In analogy with √-point electrons emitted from negative electron affinity surfaces, the majority (>50%) of the slow e⁺ leave the surface with energy ≈ φ⁺ and velocity within ～20° of the surface normal. This agrees qualitatively with the predictions of a simple 1D model.     

Global and heliolatitude indices of solar activity and cosmic ray modulation

The time variation of the galactic cosmic rays (GCR) (1958–2006) is described using solar activity indices in the form Z^α, Z^α exp[?(φ/φ₀)^β], where Z and φ are one of the solar activity indices and the heliolatitude of sunspots; α, β, and φ₀ are the optimum parameters found by the least-squares method. The time variation of the GCR flux is satisfactorily described, the role of the active region heliolatitude in the index in relation to the cosmic ray modulation is revealed.     

A remark on transition probability

Uhlmann's transition probability P(ψ, φ) of two normal states of a von Neumann algebra M, which is the supremum of |(Ψ, Φ)|² for all possible choices of representative vectors Ψ and Φ of ψ and φ, is shown to be the infimum of (∫d(μ_{ψ, e})^1/2)² for the induced measures μ_{ω, e}(B)=ω(e(B)) (B: Borel set in ℝ, ω=ψ, φ) for all possible projection-valued measures e belonging to M.     

Factorizations for self-dual gauge fields

For a particular class of patching matrices onP ₃(?), including those for the complex instanton bundles with structure group Sp(k,?) orO(2k,?), we show that the associated Riemann-Hilbert problemG(x, λ)=G?(x, λ)·G ₊ ^?1 (x, λ) can be generically solved in the factored formG _?=φ ₁ φ ₂.....φ _n . IfГ=Г _n is the potential generated in the usual way fromG _?, and we setψ _i =φ ₁.....,φ _i withψ _n =G _?, then eachψ _i also generates a selfdual gauge potentialΓ _i . The potentials are connected via the “dressing transformations” $$\Gamma _\iota = \phi _i^{ - 1} \cdot \Gamma _{\iota - 1} \cdot \phi _i + \phi _i ^{ - 1} D\phi _i$$ of Zakharov-Shabat. The factorization is not unique; it depends on the (arbitrary) ordering of the poles of the patching matrix.     

Binding-energy reference in X-ray photoelectron spectroscopy of insulators

The surface potential of a sample in XPS depends on the flux and energy of incident electrons and on the resistance, R, between the surface and the spectrometer. When R is very low, the kinetic energy E_m of the ejected photoelectron, relative to the spectrometer vacuum level, is given by the well known relation E_m=hν φ_Bφ_S, where hv is the photon energy, φ_B the binding energy relative to the sample Fermi level, and φ_S the work-function of the spectrometer. However, when R is very high and the residual charge left by the ejected photoelectron is solely compensated by a sufficient flux of low-energy monoenergetic electrons of energy φ_e, the sample charges to φ_e. The measured kinetic energy is now given by E_m = hνφ_Bφ_R+φ_e, where φ_R, is the work-function of the sample. Consequently, binding energies on insulated samples are measured relative to the vacuum level, not the Fermi level, since E_m now depends on gf_R. A good conductor can be examined both shorted and insulated. The difference in measured kinetic energy is E_m (shorted)E_m (insulated) = φ_Rφ_Sφ_e. This may provide a method for measuring changes in the work-function while monitoring surface composition.     

Localised forced ignition of globally stoichiometric stratified mixtures: A numerical investigation

Localised forced ignition of globally stoichiometric stratified mixtures (i.e. < φ > =1.0) has been analysed here based on direct numerical simulations for different initial values of velocity and equivalence ratio fluctuations (i.e. u′ and φ′), and the Taylor micro-scale l_φ of equivalence ratio φ variation. The localised ignition is accounted for by a source term in the energy transport equation which deposits energy over a stipulated time interval. It has been found that combustion takes place predominantly under premixed mode in the case of successful ignition. The initial values of φ′ and l_φ have been found to have significant effects on the extent of burning of stratified mixtures following localised ignition. It has been found that an increase in u′(φ′) has adverse effects on the burned gas mass, whereas the effects of l_φ on the extent of burning are non-monotonic and dependent on φ′. Detailed physical explanations have been provided for the observed u′, φ′ and l_φ dependences on the extent of burning in stratified mixtures.     

Dynamic-angle spinning of quadrupolar nuclei

In dynamic-angle spinning (DAS), a sample spins around an axis inclined at an angle φ(t) with respect to the magnetic field such that the averages of P_n(cos φ) are zero. The simplest case is where φ(t) assumes two discrete values φ₁ and φ₂ (complementary DAS angles) such that the averages of P₂(cos φ) and P₄(cos φ) are zero, thereby removing second-order quadrupolar (and dipolar) broadening. Examples of DAS complementary angles are φ₁ = 37.38° and φ₂ = 79.19°. Experimental details for DAS experiments are provided and applications to sodium-23 and oxygen-17 NMR illustrate the enhanced resolution achieved by removing the second-order broadening inherent in magic-angle spinning.     

Some remarks on variable range hopping—in particular in the quantum Hall regime

An expression for the heat conductivity _xx is derived in the effective medium approximation. Mott type formulas are obtained for _xx and the Peltier coefficient _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like . The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity _xx , the results are fully consistent with the experimental data on _xx and the density of states at the Fermi level. Finally, _xx is estimated which together with _xx and _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients _xx and _xy .Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation

We consider here the 1 D semilinear wave equation with a power nonlinearity and with no restriction on initial data. We first prove a Liouville Theorem for that equation. Then, we consider a blow-up solution, its blow-up curve and the set of non-characteristic points. We show that I ₀ is open and that T(x) is C ¹ on I ₀. All these results fundamentally use our previous result in [19] showing the convergence in selfsimilar variables for . This work was supported by a grant from the french Agence Nationale de la Recherche, project ONDENONLIN, reference ANR-06-BLAN-0185.     

Mean work functions effective for negative-ionic, electronic and positive-ionic emissions from polycrystalline surfaces

To elucidate the thermionic property of polycrystalline surfaces, a further study is made on the mean work functions (φ⁻, φ^e and φ⁺) effective for negative-ionic, electronic and positive-ionic emissions. Comparison between theoretical analyses and experimental data yields the conclusions as follows. (1) The equation of φ⁻ = φ^e holds always with both mono- and polycrystalline surfaces. (2) The relation of φ⁻ = φ^e < φ⁺ applies to polycrystalline surfaces because they bear the thermionic contrast (Δφ^* ≡ φ⁺ − φ^e > 0). (3) The value of Δφ^* ranges from ∼0.4 to 0.9 eV depending upon the surface species of polycrystalline metals (e.g., W, Re and Pt), whilst Δφ^* = 0 for monocrystalline surfaces. (4) When the degree of monocrystallization (δ_m) is less than ∼50%, the theoretical value of Δφ^* is virtually independent of δ_m and agrees well with experimental data, nearly the same within ±0.1 eV among the so-called “polycrystalline” surfaces of W. (5) As δ_m increases beyond ∼80 up to 100%, Δφ^* decreases rapidly down to 0 eV, showing again a good agreement between theory and experiment. (6) Our theoretical model is valid in evaluating the effective mean work functions, irrespective of the range of δ_m.     

Crossing relations for deep-inelastic and annihilation processes

We calculate in a model field theory [φ³]_σ the structure functions $\text{F}\text{?}\text{(ω), F(ω)}$ for the processes e⁺+e^?→h+X and e^?+h→e^?+X in the next to leading logarithm approximation. We find that $\text{F}\text{(ω) and F(ω)}$ satisfy the analytic continuation relation but not the Gribov-Lipatov reciprocity relation.