Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Structural and magnetic phase transitions in Pr2NiO4

Neutron powder diffraction and magnetization measurements have been performed in stoichiometric Pr₂NiO₄₊(0), which at room temperature (RT) is orthorhombic (Bmab). Ni²⁺ becomes three dimensionally (3D) antiferromagnetically ordered atT _N 325K, with a propagation vectork=[100], and spins oriented along thea axis (parallel to the propagation vector). The magnetic structure belongs to the _7g (––+)-representation (g _x mode, Shubnikov groupB _pmab') ofBmab, and a magnetic moment of 1.5 _B is measured at 155K. This compound undergoes two different structural phase transitions. First, going down in temperature, Pr₂NiO₄ transforms by a first order phase transition from orthorhombic (Bmab) to tetragonal (P4₂/ncm) atT _c1115K. At high temperature, we can predict a transformation from orthorhombic (Bmab) to tetragonal (I4/mmm) in a continuous way. The extrapolated temperature for this second structural transition isT _c21500±100K. The low temperature structural transformation allows a change in the magnetic structure which forT<T _c1 is better described in the orthorhombic symmetry. Just belowT _c1 the magnetic structure is described by the: _3g (–+)-representation ofPccn(g_xc_yf_z mode, Shubnikov groupPccn), this magnetic phase begins to disappear going down in temperature and at the same time a new magnetic phase grows. This new magnetic structure is described by the _1g ofPccn (c _xg_ya_z mode, Shubnikov groupPccn). Both magnetic structures coexist in a certain temperature range. At 1.5 K thec _xg_ya_z mode represents the total of the magnetic ordering. To reproduce the observed magnetic intensities we are forced to consider that Pr³⁺ is polarized below 40 K, with a magnetic structure which is coupled to the Ni sublattices (i.e. _1g and _3g ). The magnetic moment at low temperature for Pr is about 1.28 _B .     

Two equivalent criteria for modularity of the lattice of all physical decision effects

This paper answers the open question 1 of [3] in the affirmative and, conditionally, the open question 2 of [3], too. Assuming irreducibility of the orthomodular latticeG of all physical decision effectsE, we shall prove in the first section that modularity ofG implies symmetry of the physical probability function . In the second section, we shall consider the filter algebra (B) being assumed to possess an involution * such thatT*T=0 impliesT=0. Then this will be proved: If every atomic filterT _P is a fixpoint of * and * is, in a restricted manner, norm-preserving on the minimal left ideal _P :=(B)T _P , thenG is modular.     

Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Möbius function for the set of acyclic directed backbone graphs

Consider a two-rooted graphG, the edges of which are directed in such a way that there are no cycles and every edge belongs to some self-avoiding walk from rootu to rootv which follows the direction of the edges. Au-v backbone ofG is a subgraph formed by taking the union of any subset of directed self-avoiding walks fromu tov. Let _uv be the set of all such backbones ofG partially ordered by set-inclusion. We prove the conjecture of Bhatti and Essam that the Möbius function of this set is given, for acyclicb,b _uv withbb, by(b,b)=(–1) ^c-c , wherec andc are the respective cycle ranks ofb andb. The significance of this result in percolation theory is reviewed together with previous results for other sets of subgraphs.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

A new theory on scattering of electrons due to spiral dislocations

The topologically singular lattice structure around a spiral dislocation scatters electrons in a manner much different from the deformation-potential-scattering. Thet-matrix is represented ast(k, k)=t ₀ sin (k _z/2) exp (±i _kk/2)/sin ( _kk/2) with the scattering angle _kk, the componentk _z of the wave vector parallel to the dislocation, andt ₀(Fermi energy). This kind of scattering alone does not cause a perpendicular resistivity, but in a dirty limit a specific dislocation resistivity does exist, whose relaxation time per unit length of dislocation is of the order of/(Fermi energy).Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-KölnOn leave of absence from Department of Materials Science, Hiroshima University, Higashisenda-machi, Hiroshima, Japan     

Optical absorption zeeman spectroscopy of rare earth orthochromites

The optical absorption spectrum of Ho in HoCrO₃ in the phase ₂ (Cr:G _z F _x ; Ho:f _x c _y ) and ₄ (Cr:G _x F _z ; Ho:f _y c _x ) and the magnetization and the susceptibility of HoCrO₃ have been studied as a function of temperature and applied magnetic field. The experimental data for the Ho ground state splitting are analyzed using a molecular field approach. The analysis shows that the Cr — Ho interaction is predominantly antisymmetric exchange. The Ho — Ho interaction is of exchange as well as of dipolar origin. The phase diagram for the configurations ₂ and ₄ in theH — T plane for fieldsH y is determined in the temperature region 1.8 KT15 K.     

Superradiating 4P-4S-3P cascade of sodium vapour arising on the leading edge of the exciting laser pulse

Investigations of the superradiating cascade of sodium vapour 4P-4S-3P ₁ = 2.21 µm and ₂=1.14 µm) arising on the leading edge of the exciting laser pulse were carried out. The dependences of the actual delay time _D of the ₁ pulse on the population rise time of the laser-excited 4P state were measured and compared with those calculated following the existing theoretical model. The dependence of the actual delay time _D on the inverse density of excited atoms 1/N* is also presented. Analysis of this dependence revealed the influence of the Doppler dephasing and of the second, ₂, transition on the formation of the ₁ superradiance.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems

We consider a ferromagnetic Ising spin system isomorphic to a lattice gas with attractive interactions. Using the Fortuin, Kasteleyn and Ginibre (FKG) inequalities we derive bounds on the decay of correlations between two widely separated sets of particles in terms of the decay of the pair correlation. This leads to bounds on the derivatives of various orders of the free energy with respect to the magnetic fieldh, and reciprocal temperature . In particular, if the pair correlation has an upper bound (uniform in the size of the system) which decays exponentially with distance in some neighborhood of (,h) then the thermodynamic free energy density (,h) andall the correlation functions are infinitely differentiable at (,h). We then show that when only pair interactions are present it is sufficient to obtain such a bound only ath=0 (and only in the infinite volume limit) for systems with suitable boundary conditions. This is the case in the two dimensional square lattice with nearest neighbor interactions for 0<₀, where ₀ ^–1 is the Onsager temperature at which (,h=0) has a singularity. For >₀, (,h)/h is discontinuous ath=0, i.e. ₀=_c, where _c ^–1 is the temperature below which there is spontaneous magnetization.Research supported by AFOSR Contract # F 44620-71-C-0013.     

On the maximization of the central gravitational red-shift of a schwarzschild sphere with a given surface gravitational red-shift

Following Bondi static, spherically symmetric equilibrium configurations with a core and an envelope have been considered. It has been shown that for any configurations with nonnegative pressure and density and with a surface red-shiftz _s 4.77 arbitrarily large central red-shiftsz _c are possible in the limiting case of arbitrarily large radius. The effects of imposition of further constraints in the form of a real speed of sound not exceeding the speed of light are also examined. It is seen that for a given limiting sound-to-light-speed ratio . (i) There exists a limiting surface red-shiftz _s() 1.71. (ii) A configuration withz _s >z _s() is not possible, (iii) A configuration withz _s=z _s() has a unique and finitez _c=z _c(). (iv) Forz _s<z _s() arbitrarily large central red-shifts can be obtained for configurations with arbitrarily large radii.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Group duality and the Kubo-Martin Schwinger condition. II

Let be an invariant state of theC*-system { ,G, } on a locally compact noncommutative groupG. Assume further that is extremal -invariant for an action of an amenable groupH which is -asymptotically abelian and commutes with . Denoting byF _AB,G _AB the corresponding two point functions, we give criteria for the fulfillment of the KMS condition with respect to some one parameter subgroup of the center ofG based on the existence of a closable mapT such thatTF _AB=G _AB for allA,B . Closability is either inL (G),B(G) orC (G), according to clustering properties for . The basic mathematical technique is the duality theory for noncompact, noncommutative locally compact groups.This work is supported in part by the National Science Foundation, Grant MCS 79-03041     

Instability of two counter-streaming gyrating beams of electrons

The linear theory of the two-beam instability of weak gyrating beams is investigated. Maximum growth rates of instabilities, instability limits and frequencies of unstable waves are numerically determined. The aperiodic instability withk _{z z0}= _c( _z0 is the velocity of the beam along the magnetic field, _c is the cyclotron frequency andk _z is the longitudinal wave number) and the instability with= _c/2 and withk _{z z0}= _c/2 possess greatest growth rates. Dependence of growth rates on longitudinal and transversal components of the wave vector is investigated in detail.     

Some exact solutions to the sine-Gordon equations

We present some new exact (solitary and traveling) solutions to the sine-Gordon equationsc ²u_xx–u_tt = sinu andcu _xt+ u_tt = sinu, and the dissipative sine-Gordon equationc ²u_xx–u_tt–u_t=₁ sinu+ ₂ sin(2u). Here,, ₁, and ₂ are the coupling constants, real numbers;c is theintrinsic speed of the propagating wave determined by the system; and is the damping factor. The physical implication is briefly discussed.     

Computer simulation of the nonequilibrium critical behavior of disordered two-dimensional Ising systems

We report the results of a computer simulation of the critical relaxation of the magnetization in the two-dimensional Ising model with nonmagnetic impurity atoms frozen at the lattice sites. We assume a square lattice of dimension 400² with spin concentrationsp=1.0, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7. The Monte Carlo and dynamic renormalization group methods are used to determine the dynamical critical indexz as a function ofp: z(p): z(1)=2.24±0.07,z(0.95)=2.24±0.06,z(0.85)=2.38±0.05,z(0.8)=2.51±0.06,z(0.75)=2.66±0.07,z(0.7)=2.88±0.06. It is shown thatz(p) obeys a singular scaling law of the formz=A | ln (p–p _c) |+B withA=0.56±0.07,B=1.62±0.07.Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 83–88, August, 1994.     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).