Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Unitarity bounds for 4-fermion contact interactions

In this paper we consider the effect of unitarity bounds s_bs(E₁+E₂) _cms ² for the recently proposed types of nonderivative 4-fermion contact interactions. To this purpose we decompose the helicity amplitudes at c.m.s. into partial waves. The bounds are defined to hold for all reaction channels due to the same type of contact interaction. We find s_b=4/. Here is the coupling constant. The factor depends on the type of coupling and on the different cases to identify the fermions. It ranges from 1/3 to 4.     

D=2 and D=4 realization of κ-conformal algebra

We describe the generators of-conformal transformations leaving invariant the-deformed d'Alembert equation. For the case D=4 the algebraic structure of the conformal extension of the off-shell spin zero realization of-Poincaré algebra is discussed. Then the D=2 off-shell realization of-conformal algebra for arbitrary spin and its commutation relations are studied.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2P 302 087 06.     

Ward's identity in critical dynamics

We consider the relaxation of an order-parameter fluctuation of wave numberk in a system undergoing a second-order phase transition. In general, close to the critical point, wherek ^{–1 –1} (the correlation length) the relaxation rate has a linear dependence on/k of the form (k, ) = (k, 0)x(1–a/k). In analogy with the use of Ward's identity in elementary particle physics, we show that the numerical coefficienta is readily calculated by means of a mass insertion. We demonstrate, furthermore, that this initial linear drop is the main feature of the full/k dependence of the scaling functionR ^–x (k,), wherex is the dynamic critical exponent andR=(k²+ ²)^1/2 is the distance variable.     

Phonon anomalies and martensitic transitions in bcc materials

The general systematics of phonon spectral anomalies are considered for materials with bcc and B2 structures. In a model of central pair-wise interactions, it is shown that anomalies on the TA₂ branch at =1/3 (211), the LA phonon branch at =2/3 (111), and on the TA branch at =1/2 (111) arise simultaneously with the softening of the shear elastic moduli C' and C₄₄. The TA phonon anomaly at =1/3 (110) is not due to softening of the elastic moduli, but rather is due to the long range nature of the pair-wise or multiparticle interaction. A model is proposed for the nucleation of the martensitic phase for B2 compounds, the distinctive feature of which is a consideration of the softening of the shear moduli, which is modulated by lattice relaxation around ordering defects, along with the possibility of additional defect ordering near the transition.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 10, pp. 31–39, October, 1993.     

Thermal conductivity and specific heat of amorphous Zr0.67Ni0.33 after structural relaxation

Low-temperature measurements of the thermal conductivity (0.3KT5K) and of the specific heatC (0.07KT3.5K) of splat-cooled amorphous superconducting Zr_0.67Ni_0.33(T _c 2.7K) after different annealing stages are reported. increases progressively (up to 55%) after annealing. An analysis of with the help of normal-state measurements belowT _c in an overcritical field shows that the phonon-electron scattering remains unaltered after annealing. Hence the increase in must be entirely attributed to structure-induced (intrinsic) scattering, i.e. by two-level tunneling states (TLS) at low temperatures (T1K). The specific heat shows a small decrease aboveT _c (by 8%) which is attributed to a small diminution of the electronic density of states at the Fermi level and to a small increase in the Debye temperature. ForTT _c where TLS dominate, the specific heatC decreases less upon annealing than expected from the increase of in the standard tunneling model. This points to a change in the TLS relaxation time spectrum upon annealing, as observed previously for Zr _x Cu_1–x glasses.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of electric or magnetic type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an antiparticle. Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (, ₀, ,l, m), where ₀ is the mean of the angular frequencies of the plane waves making up the configuration, is the variance of those frequencies, is a positive constant with dimensions of action, andl, m are angular momentum quantum numbers withl a positive integer andm an integer such that ml. The rest energy of the particle is ₀, its spin is m, and its lifetime is of the order of 1/. Its antiparticle has ₀ replaced by –₀.     

Correlated majority model

We extend the bichromatic majority model by including (one-dimensional isotropic) correlations and numerically discuss, through Monte Carlo simulations, the simple, 1/3, and 2/3 majority rules. We calculate, as functions of the concentration and correlation degree, the mean finite cluster size, and the order parameterm as well as their respective critical exponents and. We find1 regardless of the correlation degree or the type of majority. Also, a supplementary divergence of is observed at the>0 borderline.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Excitation of low-frequency waves in the topside ionosphere in heating experiments at the leading edge of accelerated suprathermal electron beams

We consider the excitation of low-frequency waves in the upper ionosphere at the leading edge of suprathermal electron beams produced in the reflection region of a powerful radio wave. The integral growth rate of electron-beam instability is found for a wave packet intersecting an instability domain. The growth rate is strongly dependent on the ratio R=(/ ) /(/ )of the group velocity of the wave packet along the geomagnetic field to its phase velocity, which is equal to the velocity of the resonant particles. It is shown that in the upper ionosphere (the electron gyrofrequency f _Be 1MHz and the ratio of ion to electron masses M/m=18364the growth rate of longitudinal lower-hybrid oscillations is maximal at the frequency f 200kHz when R 1and the phase velocity / begins to grow due to the influence of ions. The excitation of longitudinal oscillations with f < f _Bi increases with decreasing f, since the ratio R approaches unity in this case. The enhancement of ion cyclotron oscillations is most effective in the vicinity of the second ion cyclotron harmonic f<2f _Bi 1MHz. Magnetohydrodynamic (MHD) waves interact with higher-energy particles having velocities on the order of the Alfvén velocity V _A ~ 10⁸ cm/sec. This interaction is damped in the small parameter (m/M)=1/1836.However, the integral growth rate of low-frequency Alfvén waves becomes considerable in the case of their quasiorthogonal (with respect to the magnetic field) propagation ( )in a strongly magnetized ionospheric plasma when the Alfvén velocity is much greater than the thermal velocity of the electrons. The interaction of a fast magnetosound (FMS) wave with resonant electrons increases considerably for f f _Bi when R=1and the wave packet moves along the magnetic field with resonant particle velocity (this condition is similar to the well-known R. Gendrin condition obtained earlier for high-frequency whistlers excited by higher-energy electrons). The magnitude and direction of the vector of the FMS wave as a function of its frequency f are found for R=1. The possibility of using these processes for explanation of the same features of low-frequency waves excited in heating experiments is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 2, pp. 163–178, February, 1996.This work was supported in part by the Russian Foundation for Fundamental Research.     

The bicovariant differential caculus on the κ-Poincaré and κ-Weyl groups

The bicovariant differential calculus on four-dimensional -Poincare group and corresponding Lie-algebra like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional -Weyl group and corresponding Lie-algebra like structure for any metric tensor in the reference frame in which g ₀₀ = 0 are considered.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

The semi-conducting properties of CdSnAs2

The paper gives the results of measuring the temperature dependence of the electrical conductivity(T), the Hall coefficientR _H (T) and the magnetic susceptibility(T) forn-type CdSnAs₂. The effective mass of the electrons was determined by analysis of the measured dependences on the basis of the simple theory for an isotropic non-degenerate semi-conductor. It was found to bem _n /m ₀=2×10^–2 in the intrinsic region and does not depend on the temperature; the energy gap ise _g ⁰=0·26 eV and the molar susceptibility of the CdSnAs₂ lattice _G ^mol=–112× ×10^–6. The mobility of the electrons in the intrinsic region reaches a value of _n =25 000 cm²V^–1sec^–1 at 500°K and decreases exponentially _n T ^–1.67 with rising temperature. The density of CdSnAs₂ was determined pyknometrically,g9=5·35 g cm^–3. The measurements were made on ann-type polycrystalline sample consisting of crystals a few millimetres in diameter, which at a temperature of 100°K had a free electron concentration ofn _s =6×10¹⁶ cm^–3.

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CdSnAs₂

(T), R _H (T) (T) CdSnAs₂ . m _n /m ₀= =2.10^–2, ; E _G ⁰=0,26 eV, CdSnAs_{2 G} ^mol= =–112.10^–6. 500°K _n =25 000 cm²V^–1sec^–1 , _n T ^–1,67. CdSnAs₂ =5,35 g cm^–3. , , 100°K n _s =6.10¹⁶cm^–3.

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The authors would like to thank Mr. P. Jansa for help in measuring the temperature dependence of the magnetic susceptibility.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

Electron velocity and momentum density

A null 4-vector ^°, based on Dirac's relativistic electron equation, is shown explicitly for a plane wave and various Coulomb states. This 4-vector constitutes a mechanical model for the electron in those states, and expresses the important spinor quantities represented conventionally byn, f, g, m, j, ,1, ands. The model for a plane wave agrees precisely with the relation between velocity and phase gradient customarily used in quantum theory, but the models for Coulomb states contradict that relation.     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.     

Existence of Baryons,Baryon Spectrum and Mass Splitting in Strong Coupling Lattice QCD

We consider a functional integral formulation for one-flavor lattice Quantum Chromodynamics in d=2,3 space dimensions and imaginary time, and work in the regime of the small hopping parameter , and zero plaquette coupling. Following the standard construction, this model exhibits positivity which is used to obtain the underlying physical Hilbert space . Then, using a Feynman-Kac formalism, we write the correlation functions for the model as functional integrals over the space of Grassmannian (fermionic) fields for one quark specie and the SU(3) gauge fields. We determine the energy-momentum spectrum associated with gauge invariant local baryon (anti-baryon) fields which are composites of three quark (anti-quark) fields. With the associated correlation functions, we establish a Feynman-Kac formula, and a spectral representation for the Fourier transform of the two-point functions. This representation allows us to show that baryons and anti-baryons arise as tightly bound, bound states of three (anti-)quarks. Labelling the components of the baryon fields by s=3/2,1/2,-1/2,-3/2, we show that the baryon and anti-baryon mass spectrum only depends on |s|, and the associated masses are given by M_s= –3ln+r_s(), where r_s() is real analytic in , for each d=2,3. The mass splitting is M_3/2–M_1/2=18⁶, for d=2 and, if any, is at least of (⁷), for d=3. In the subspace _o generated by an odd number of fermions, the baryon and anti-baryon energy-momentum dispersion curves are isolated up to near the baryon-meson threshold –5ln (upper gap property), identical and are determined up to (⁵). The symmetries of coordinate reflections, spatial lattice rotations, parity and charge conjugation are established for the correlation functions, and are shown to be implemented on by unitary (anti-unitary, for time reversal) operators.