The affine geometry of the Lanczos H-tensor formalism

We identify the fiber-bundle-with-connection structure that underlies the Lanczos H-tensor formulation of Riemannian geometrical structure. We consider linear connections to be type (1,2) affine tensor fields, and we sketch the structure of the appropriate fiber bundle that is needed to describe the differential geometry of such affine tensors, namely the affine frame bundleA ₁ ² M with structure groupA ₁ ² (4) =GL(4) T ₁ ^{2 4} over spacetimeM. Generalized affine connections on this bundle are in 1-1 correspondence with pairs(, K) onM, where thegl(4)-component denotes a linear connection and the T ₁ ^{2 4}-componentK is a type (1,3) tensor field onM. We show that the Lanczos H-tensor arises from a gauge fixing condition on this geometrical structure. The resulting translation gauge, theLanczos gauge, is invariant under the transformations found earlier by Lanczos. The other Lanczos variablesQ _mandq are constructed in terms of the translational component of the generalized affine connection in the Lanczos gauge. To complete the geometric reformulation we reconstruct the Lanczos Lagrangian completely in terms of affine invariant quantities. The essential field equations derived from ourA ₁ ² (4)-invariant Lagrangian are the Bianchi and Bach-Lanczos identities for four-dimensional Riemannian geometry.     

Lanczos Potential for the van Stockung Space-Time

The Lanczos Potential is a theoretical useful tool to find the conformal Weyl curvature tensor C _abcd of a given relativistic metric. In this paper we find the Lanczos potential L _abc for the van Stockung vacuum gravitational field. Also, we show how the wave equation can be combined with spinor methods in order to find this important three covariant index tensor.     

The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions

We prove that a Lanczos potential L _abc for the Weyl candidate tensor W _abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L _abc and W _abcd, then this system's integrability conditions should be checked, and so on. When we find a non-trivial condition involving only W _abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L _abc.     

Resonances in the KSKSKL system produced in collisions of negative pions with a carbon target at a momentum of 40 GeV

The experimental spectrum of the K _S K _S K _L system from the reaction π ⁻C → K _S K _S K _L + Y at amomentum of 40 GeV was obtained experimentally with the aim of studying resonance states featuring open strangeness and occurring in the high-mass region. The experiment was performed at the 6-m spectrometer installed at the Institute for High Energy Physics (IHEP, Protvino). The spectrum displays, along with well-known resonances [K ₁(1640), K ₂(1770), K ₂(1820), K ₂(1980)], which fit in the quark-antiquark classification, the exotic resonances K ₂(2280) and K ₄(2500). The K ₂(2280) resonance exhibits the properties of a hybrid and has an exotic decay mode producing a triplet of known resonance states related to each other by quark-gluon mixing. The mechanism of the formation of the observed hybrid K ₂(2280) is dominated by the exchange of a natural spin-parity in the t channel of the reaction. The mode of decay into f ₀(980)K _L and the mode of decay into f ₂(1270)K _L are observed for the K ₂(1770) and the K ₂(1980) resonance, respectively. __________ Translated from Yadernaya Fizika, Vol. 66, No. 5, 2003, pp. 860–867. Original Russian Text Copyright ? 2003 by Tikhomirov, Erofeev, Erofeeva, Luzin.     

Measurement of K β K /α values using proton beamvalues using proton beam

The Measurement of K _β K _/α intensity ratios are measured in some 3d shell elements by using a 2 MeV proton beam along with a high resolution Si(Li) detector. The present Measurement of K _β K _/α intensity ratios are in good agreement with Scofield modified theoretical values, thus supporting the basic assumptions in that theory. From the present Measurement of K _β K _/α intensity ratios, it is evident that due to chemical effects, the experimental Measurement of K _β K _/α intensity ratios will be increased while they will be decreased due to the presence of simultaneous M-shell vacancies which are produced due to proton excitation.     

A small-parameter approach for few-body problems

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K ₀. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K ⩽ K ₀. Contributions from states with K>K ₀ are taken into account in a closed form, i.e., without an expansion over basis functions. Estimates concerning the efficiency of the approach are presented. The text was submitted by the author in English.     

Concentrated Kondo systems

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T _K CKS (T _K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (～k _B T _K) high-amplitude Abrikosov-Suhl resonance E _R in the vicinity of the Fermi level E _F. This resonance is situated exactly at E _F in low T _K CKS with T _K < Δ_CF and near E _F in high T _K CKS with T _K > Δ_CF (Δ_CF is the crystal field splitting). In low T _K ‘j=1/2’ CKS the condition E _R=E _F leads to an increase of the density of states at E _F, which is large enough to induce heavy fermion superconductivity in CeCu₂Si₂, UBe₁₃. We demonstrate that the transition from low T _K (E _R=E _F) to high T _K CKS (E _R≠E _F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition. It appears that in many cases the essentially non-integer valence state of the rare-earth elements in metallic compounds is thermodynamically unstable with respect to a transition to an almost integer valence state, because it realizes the maximum gain in free energy from the Kondo condensation.     

Determination of the negative ion yield of copper sputtered by cesium ions

Abstract

This paper describes the determination of secondary ion yields for negative ions obtained by bombardment of copper by cesium ions. Stable and reproducible surface conditions are reached by high rate sodium deposition simultaneously with sputtering. An optimum thickness of sodium corresponding to about one monolayer is found. Total negative ion yields K ^? _Σ are measured by a double modulation technique. Individual negative ion yields K ^? _i are then found by mass spectrometrically determining the various negative ion intensities, the sum of which relates linearly to K ^? _Σ. This method is based on the assumption of an equal angular and energy distribution of all sputtered negative ions. Data are given for K^? _Σ and K ^? _Cu and K^? _O. The dependence of K ^? _i on primary ion energy (500 to 2500 eV) is similar to ordinary sputtering which points to the same basic mechanism in both cases.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

A method for determination of higher-order magnetic anisotropy constants — Importance of the cubic K3 and K4 for certain energy levels models

A method for determination of magnetocrystalline anisotropy constants of arbitrary order is proposed. The method is based on a least squares fitting of a phenomenological anisotropy energy for a given symmetry truncated at an arbitrary order term to a theoretical anisotropy energy computed exactly for a given energy level model. Several applications of the method to cubic systems are considered. The study reveals that the widely used expressions in the literature for the cubic constants K₁ and K₂ in terms of free energy for the three symmetry direction are of rather limitedvalidity only. The higher-order cubic constants K₃, K₄ and K₅ are determined besides the usual K₁ and K₂ in temperature range 0 to 300 K. The importance of the higher- order terms with respect to the first term in the cubic anisotropy energy is discussed. The results show that the cubic constants K₃ and K₄ cannot be neglected for most of the energy level models studied at certain temperatures.     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Spatial characteristics of Kα radiation from weakly relativistic laser plasmas

The spatial dependence of K _α emission generated from laser-produced hot electrons is investigated experimentally and theoretically. In addition, the conversion efficiency of K _α production as a function of laser intensity is measured and compared with modeling results. We use the terawatt Ti:sapphire laser at MPQ and vary the peak intensity from 10¹⁵ to 10¹⁸ W/cm² with a pulse duration of 200 fs. A solid Cu target is placed at various positions in the laser focus, which allows one to vary the intensity but keep the total energy on the target constant. When the target is near best focus, the FWHM of the K _α emission, measured using a knife-edge, is considerably larger than the FWHM of the laser intensity. In measuring the efficiency of K _α production using the fundamental wavelength of the laser, a clear maximum of K _α emission is observed at a position away from best focus, where the peak intensity is down by more than an order of magnitude from the value at best focus. When the second harmonic of the laser is used, the K _α emission is peaked near best focus. The K _α emission from layer targets is used to obtain an estimate of the temperature of the hot electrons. Modeling of K _α production, using a Monte Carlo electron/photon transport code, shows the relationship between incident electron energy and the emitted K _α emission. Efficient K _α generation from the low-intensity wings of the laser pulse contributes to the large spot size of the K _α emission. The lower electron temperatures that are expected for the second harmonic explain the differences in the location of maximum K _α emission for the two wavelengths. We discuss the use of K _α emission in photoionizing inner-shell electrons with the goal of achieving X-ray lasing at short wavelengths. Received: 6 April 1999 / Revised version: 31 May 1999 / Published online: 11 August 1999     

Fe39.4－xCo40Si9B9Nb2.6Cux纳米晶合金的有效磁各向异性研究

采用多晶材料趋近饱和定律研究了非晶Fe_39.4-xCo₄₀Si₉B₉Nb_2.6Cu_x(x=0.5,1,1.5) 合金在不同温度纳米晶化后的有效磁各向异性常数〈K〉.结果表明， Cu含量较低(x=0.5)时，纳米晶粒较大并且在较低的退火温度(550℃)下析出硬磁相，〈K〉随退火温度T_a升高显著增加；随着Cu含量的增加，有效地细化了晶粒，并且抑制了硼化物的析出，〈K〉明显减小.讨论了〈K〉与晶粒尺寸D及初始磁导率的关系. 关键词： 纳米晶 有效磁各向异性 磁导率 FeCo基合金     

On the parameters of the magnetocrystalline anisotropy of U3P4 and U3As4 single crystals

Conclusion The change from the zero to the first approximations is accompanied by the change of the sign ofK ₁,K ₂ ¹ being of the same order asK ₁ ¹ . It implies that the neglection of further members of the expansion in (2) may not be quite right. Therefore it might be better to take into consideration also the effect of the further members in (5), but in such a case equation (7) would contain so many unknown parametersK _i ^j , that another way how to solve it would be necessary. In our case, (7) is an equation of a tangent to the curveK ₁ ⁰ =f(1–x ²) at const.H, which has enabled us to determine the dependencesK ₁ ¹ (T, H) andK ₂ ¹ (T, H). Generally, there are other methods of studying the parametersK _i ^j (based on the analysis of torque curves for example) which are more suitable in similar cases, but these methods usually allow necessary measurements only in the fields considerably less than those used in [5].     

Determination of Chemical Effect on the Kβ1/Kα, Kβ2/Kα, Kβ2/Kβ1 and Kβ/Kα X-Ray Intensity Ratios of 4d Transition Metals

It is clear that detailed studies performed under identical experimental conditions are desirable to determine the effect of the chemical environment on the value of intensity ratios. To better understand this effect, we conducted measurements on Kβ₁/Kα, Kβ₂/Kα, Kβ₂/Kβ₁ and Kβ/Kα x-ray intensity ratios. The Kα and Kβ_1,2 emission spectra for compounds of 4d transition metals Y, Zr, Nb, and Mo were measured using a Si(Li) solid-state detector. The samples were excited by 22.69 keV x-rays emitted from a ¹⁰⁹Cd radioisotopes source. The experimental results for pure elements are compared with the other experimental and theoretical values.     

A study of mixed mode fracture by photoelasticity and digital image analysis

In this paper, the results from two experimental methodologies, photoelasticity aided by digital image processing and precision digital image correlation, are presented for a mixed mode fracture problem. The mixed mode fracture problem was a three-point-bend edge-crack specimen which was loaded at various off-crack-line locations between the crack line and the specimen support line. The estimations of K_I and K_II from both methodologies indicate that the crack tip stress field is strongly intensified by K_I but not K_II.     

Witten–Reshetikhin–Turaev Invariants of¶Seifert Manifolds

For Seifert homology spheres, we derive a holomorphic function of K whose value at integer K is the sl ₂ Witten–Reshetikhin–Turaev invariant, Z _K , at q= exp 2πi/K. This function is expressed as a sum of terms, which can be naturally corresponded to the contributions of flat connections in the stationary phase expansion of the Witten–Chern–Simons path integral. The trivial connection contribution is found to have an asymptotic expansion in powers of K ⁻¹ which, for K an odd prime power, converges K-adically to the exact total value of the invariant Z _K at that root of unity. Evaluations at rational $K$ are also discussed. Using similar techniques, an expression for the coloured Jones polynomial of a torus knot is obtained, providing a trivial connection contribution which is an analytic function of the colour. This demonstrates that the stationary phase expansion of the Chern–Simons–Witten theory is exact for Seifert manifolds and for torus knots in S ³. The possibility of generalising such results is also discussed. Received: 26 October 1998 / Accepted: 1 March 1999     

GeneralizedK-flows

The classical concept ofK-flow is generalized to cover situations encountered in non-equilibrium quantum statistical mechanics. The ergodic properties of generalizedK-flows are discussed. Several non-isomorphic examples are constructed, which differ already in the type (II₁, III, and III₁) of the factor on which they are defined. In particular, generalized factorK-flows with dynamical entropy either zero (singularK-flows) or infinite (special non-abelianK-flows) are constructed.On leave of absence from the Depts. of Mathematics and Physics, The University of Rochester, Rochester, N. Y. 14627, USA     

Analysis of the boundary problem of SSWR in asymmetric isotropic insulator films

The influence of various combinations of the uniaxial surface anisotropy constantsK _s1 andK _s2 on the angular dependence of the standing spin-wave resonance (SSWR) spectrum is studied for an isotropic insulator film with asymmetrically pinned spins. It is shown that the (K _s1,K _s2)-plane can be divided into zones in which the angular dependence of the SSWR spectrum has different characteristic features. These features are studied in detail.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

Strangeness conservation and pair correlations of neutral kaons with close momenta produced in inclusive multiparticle processes

The phenomenological structure of inclusive cross sections of the production of two neutral K mesons in collisions of hadrons and nuclei is investigated taking into account the strangeness conservation in strong and electromagnetic interactions. The relations describing the dependence of the correlations of two short-lived and two long-lived neutral kaons K _S ⁰ K _S ⁰ , K _L ⁰ K _L ⁰ and the correlations of “mixed” pairs K _S ⁰ K _L ⁰ at small relative momenta upon the space-time parameters of the generation region of K ⁰ and mesons, which involve the contributions of Bose statistics and S-wave strong final-state interaction, have been obtained. It is shown that, under the strangeness conservation, the correlation functions of the pairs K _S ⁰ K _S ⁰ and K _L ⁰ K _L ⁰ , produced in the same inclusive process, coincide, and the difference between the correlation functions of the pairs K _S ⁰ K _S ⁰ and K _S ⁰ K _L ⁰ is conditioned by the production of the pairs of nonidentical neutral kaons K ⁰ . The text was submitted by the authors in English.