QCD sum rule determination of the axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, g_A(T). We find that g_A(T) is essentially independent of T, in the very wide range 0≤T≤0.9 T_c, where T_c is the critical temperature. While g_A at T=0 is q²-independent, it develops a q² dependence at finite temperature. We then obtain the mean square radius associated with g_A and find that it diverges at T=T_c, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.     

Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth

Highly accurate direct numerical simulations have been performed for two-dimensional free-surface potential flows of an ideal incompressible fluid over a constant depth h, in the gravity field g. In each numerical experiment, at t = 0 the free surface profile was in the form y = A ₀cos(2πx/L), and the velocity field v = 0. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes A ₀ ≲ 0.12h and spatial periods at least L ≲ 120h. The time of recurrence T _FPU is well fitted by the formula T _FPU(g/h)^1/2 ≈ 0.16(L/h)²(h/A ₀)^1/2.     

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Fermion Fields in Theories of Gravitation

After an introduction to the formalism used throughout the paper there follows a concise presentation of the theory of fermion fields in one-tetrad gravitational theories. That presentation gives a hint to the construction of a bi-tetrad theory, the two tetrad fields being denoted by h^A_k and h?^A_k. The tetrad field h^A_k. gives the Riemannian metric g_kl while the tetrad field h?h^A_k is orthonormalized with respect to the flat metric a_kl. Specializing h?^A_k in such a way that they have the form δ^A_k in the preferred coordinates of Minkowski space and using a matter Lagrangian which contains these h?^A_k only by the anholonomic components of the metric Christoffel symbols, we obtain a dynamical energy momentum tensor which is equal to the canonical one. Then we consider the relations of the bi-tetrad theory to other theories which are only covariant with respect to global Lorentz transformations from the beginning. As an example we formulate the main relations of the two-component neutrino theory.     

Method of Quantum Characters in Equivariant Quantization

 Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 _h (M) is a 𝕌 _h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 _h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 _h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌^* _h (g) and quotients of 𝔸 _h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 _h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ ⁿ ), and 𝔸 _h (M) the so-called reflection equation algebra associated with the representation of 𝕌 _h (g) on ℂ ⁿ . For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits. Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003 RID="*" ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01. Communicated by L. Takhtajan     

Classical and quantum duality in Jordanian quantizations

We prove that for the first order coboundary deformation of a Lie bialgebra (g, g₁ ^*) (g, g₁ ^* + g₂ ^*) one can always get the quantized Lie bialgebra A(g, g₂ ^*) as a limit of the sequence of quantizations of the type A(g, g₁ ^*).     

(GL(<Emphasis Type="Italic">n</Emphasis> + 1, ℝ), GL(<Emphasis Type="Italic">n</Emphasis>, ℝ)) is a generalized Gelfand pair

Denote by G = GL(n + 1, ℝ) the group of invertible (n + 1) × (n + 1) matrices with real entries, acting on ℝ ⁿ⁺¹ in the usual way, and let H ₁ = GL(n, ℝ) be the stabilizer of the first unit vector e ₀. Let H ₀ = GL(1, ℝ) and set H = H ₀ × H ₁. It is known that the pair (G,H) is a generalized Gelfand pair. Define a character χ of H by χ(h) = χ(h ₀ h ₁) = χ0(h ₀) where χ0 is a unitary character of H ₀ (h ₀ ∈ H ₀, h ₁ ∈ H ₁). Let σ be the anti-involution on G given by σ(g) = ^t g. In this note, we show that any distribution T on G satisfying T(h ₁ gh ₂) = χ(h ₁ h ₂) T(g) (g ∈ G; h ₁, h ₂ ∈ H) is invariant under the anti-involution σ. This result implies that (G,H ₁) is a generalized Gelfand pair.     

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n _h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n _h (A, t) = 2c _h /(A + λ _h t)², demonstrating the validity of dynamical scaling in this system. Here $ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-0em} 8}\pi \sqrt 3 $ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ _h is a material parameter. The distribution of domain areas, n _d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ _h t. Identical forms are obtained for coarsening from a critical initial state, but with c _h replaced by c _h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c _h . By applying a ‘mean-field’ type of approximation we obtain the form n _d (A, t) ? 2c _d [λ _d (t+t ₀)] ^τ?2/[A+λ _d (t+t ₀)] ^τ , where t ₀ is a microscopic timescale and τ = 187/91 ? 2.055, for a disordered initial state, and a similar result for a critical initial state but with c _d → c _d /2 and τ → τ _c = 379/187 ? 2.027. We also find that c _d = c _h + O(c _h ² ) and λ _d = λ _h (1 + O(c _h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Spherical Symmetric Solution in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Model Around Charged Black Hole

A static, asymptotically flat, spherically symmetric solutions is investigated in f(R) theories of gravity for a charged black hole. We have studied the weak field limit of f(R) gravity for the some f(R) model such as f(R)=R+ε h(R). In particular, we consider the case lim  _R→0 h(R)/h′(R)→0 and find the space time metric for f(R)=R+[(m⁴)/(R)]f(R)=R+{\mu^{4}\over R} and f(R)=R ^1+ε theories of gravity far away a charged mass point.     

On the high spin expansion in the SYM theory

We study the form of the high spin expansion of the minimal anomalous dimension for long operators belonging to the sl(2) sector of SYM. Keeping fixed the ratio j between the twist and the logarithm of the spin, the minimal anomalous dimension expands as γ(g,j,s)=f(g,j)lns+f⁽⁰⁾(g,j)+O(1/lns). This particular double scaling limit is efficiently described, including the desired accuracy O((lns)⁰), in terms of a linear integral equation. By its use, we are able to evaluate both at weak and strong coupling the subleading scaling function f⁽⁰⁾(g,j) as a series in j, up to the order j⁵. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.     

Correction of Cosmological Expansion to Angular Deflection of Light and Radar Echo Delay

The angular deflection of light and radar echo delay are famous results predicted by general relativity. The gravitational lensing problems depend on the deviation of light from its straight line path in its basic equation. Using the Robertson-McVittie spacetime metric, which coincides thoroughly with the Schwarzschild metric in the isotropic coordinate and the FLRW metric for curvature parameter k=0 when M=0, we discuss the correction of cosmological expansion to the angular deviation of light path and the radar echo delay. The deviation terms arising from the expansion of universe are found to be simply -\frac4GMr_minc²(\fracH₀²2c²r_min²)-\frac{4GM}{r_{\mathit{min}}c^{2}}(\frac{H_{0}^{2}}{2c^{2}}r_{\mathit{min}}^{2}) for angular deviation and \frac2H₀²3c³(r_A³+r_B³)\frac{2H_{0}^{2}}{3c^{3}}(r_{A}^{3}+r_{B}^{3}) for radar echo delay.     

Nominal source of the Kruskal metric

Takingds ²=–f (u, v)dudv+r ²(u, v)d²as the generic form of the metric from the out-set, a singular energy momentum tensor is determined which may formally be regarded as the source of the Kruskal metric. The result obtained is in harmony with the earlier work of Tangherlini.     

Effect of magnetic field on luminescence of MgS,CaS and CaO phosphors activated with Bi3+ ions

The magnetic field dependence of the intensity I(A₀) of the zero-phonon line of the ³A_1u → ¹A_1g emission band is measured at 4.2 K for MgS, CaS and CaO phosphors activated with Bi³⁺ ions. The increase in I(A₀) is proportional to the square of the external magnetic field. The results are compared with those for Pb²⁺-activated phosphors.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Acoustic scattering by an impenetrable spheroid

The scattering of a plane acoustic wave from an impenetrable, soft or hard, prolate or oblate spheroid is considered. Two different methods are used for the evaluation. In the first, the pressure field is expressed in terms of spheroidal wave functions. In the second, a shape perturbation method, the field is expressed in terms of spherical wave functions only, while the equation of the spheroidal boundary is given in spherical coordinates. Analytical expressions are obtained for the scattered pressure field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = d/(2a) , where d is the interfocal distance of the spheroid and 2a is the length of its rotation axis. In this case, exact, closed-form expressions are obtained for the expansion coefficients g ⁽²⁾ and g ⁽⁴⁾ in the relation S(h) = S(0)[1 + g ⁽²⁾ h ² + g ⁽⁴⁾ h ⁴ + O(h ⁶)] expressing the scattered field and the scattering cross-sections. Numerical results are given for various values of the parameters. Published in Russian in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 4, pp. 500–513. The text was submitted by the authors in English.     

MCD spectroscopy of transition metal ions in fluoride crystals

Absorption spectra of crystals of KZn _x Fe_1-x F₃ (0·006 < 1 - x < 0·07) have been measured in order to obtain information about Fe²⁺-F^--Fe²⁺ pairs. However, by means of high resolution MCD spectroscopy, it has been established that very small amounts of Fe³⁺ are present in the crystals. The absorption spectra then show features which are due to (a) Fe²⁺, (b) Fe³⁺ and (c) Fe²⁺, Fe³⁺ pairs. In addition to the characteristic Jahn-Teller split ⁵ T _2g → ⁵ E_g band of Fe²⁺, there is a weak, spin-allowed, vibronically assisted transition near 40 000 cm^-1, which is assigned to ⁵ T _2g (d⁶) → ⁵ A _1g (d⁵s). The MCD of this band is consistent with this assignment. The remainder of the visible and near ultra-violet absorption intensity is associated with Fe²⁺/Fe³⁺ pairs. Most of the bands are due to excitations localized on the Fe²⁺ though some weaker ones are assigned as excitations to ⁴ A _1g on the Fe³⁺ of the pair. There is also a strong, broad underlying absorption probably due to t _2g → t _2g charge transfer in the pair.