Representations of central extensions of differentiably simple lie superalgebras

LetS be a simple Lie algebra of characteristic 0 and (n) be the Grassmann superalgebra inn indeterminates. We can form the Lie superalgebraS (n). The purpose of this paper is to classify all finite dimensional irreducible representations of all central extensions ofS (n). We will also give a character formula for these representations.     

On the effect of impurities on the critical resolved shear stress of zinc single crystals

The dependence of the critical resolved shear stress of zinc single crystals on the impurity content and the dislocation density is observed. It is shown that the effect of impurities on the critical resolved shear stress is indirect.

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A refinement of Simon's correlation inequality

A general formulation is given of Simon's Ising model inequality: whereB is any set of spins separating from . We show that _b can be replaced by _{b A} whereA is the spin system insideB containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01     

Precipitation sequences and transformation kinetics in the Al-30 wt.% Zn alloy aged below 160°C

The transformation sequences in the Al-30 wt.% Zn alloy aged below 160 °C have been investigated by X-ray diffraction and transmission electron microscopy. The sequence G.-P. zones _R has been observed between 85 and 161 °C, whereas the direct G.-P. zones to-transformation occurs below 85 °C. The identical isothermal growth kinetics of both the G.-P. zones and the _R -precipitates was found. The log-log plots yielding a set of parallel straight lines from 50 to 150 °C indicate no change in the activation energy of growth of both these precipitates. The change in the precipitation sequence led to the change in the transformation kinetics. The T-T-T curves have been measured for the formation of metastable _R -phase and for the completion of ellipsoidal G.-P. zones or of _R to-transformation. The retardation in reaching equilibrium found below 85 °C was associated with the observed change in the transformation sequence. This was explained by the different accommodation of the misfit at the interfaces between G.-P. zones or _R -precipitates and the-matrix.The authors are much indebted to Doc. Dr. V.Syneek, CSc. for stimulating discussions. Our thanks are also due to Ing. V.íma and Mr. P.Vyhlídka for the preparation and careful chemical analyses of the investigated samples. The assistance of Mr. Z.iký and Mr. V.Petr in X-ray diffraction measurements and the heat-treatment of samples is appreciated.     

Lorentz-symmetric solutions of nonlinear equations

Asymptotic properties of a real scalar self-interacting classical field depending on one variablez = t ²–x ² are studied. The field(z) approaches a minimum of the potentialU() for z + and a maximum forz– ifU((0)) is larger than two minima and smaller than two maxima ofU neighbouring to(0).Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Hölder Equicontinuity of the Integrated Density of States at Weak Disorder

Hölder continuity, |N(E)–N(E)| C |E – E|, with a constant C independent of the disorder strength is proved for the integrated density of states N(E) associated to a discrete random operator H=H_o + V consisting of a translation invariant hopping matrix H_o and i.i.d. single site potentials V with an absolutely continuous distribution, under a regularity assumption for the hopping term.Mathematics Subject Classifications (2000). 82D30, 46N55, 47N55.     

Brueckner calculations in harmonic oscillator basis

The binding energy (b.e.), r.m.s. radius and charge form factor of the⁴He nucleus are calculated for the Hamada-Johnston potential using the method developed in part I of this study. The single-particle spectrum is derived from that of a harmonic oscillator by means of an overall shiftC and state-dependent shifts _h of occupied levels. The's are chosen self-consistently and the dependence of results onC and oscillator frequency is examined. Third-order diagrams in the BG expansion for energy are explicitly calculated (except those belonging to the three-particle cluster) and their importance for getting a weak dependence of the b.e. onC is demonstrated. Dependence on remains rather strong; arguments are given in favour of the choice of that minimizes second-order diagrams. Effects due to the motion of the centre of mass of the nucleus are eliminated by subtracting T _CM calculated up to the second order, the usual zero-order approximation of T _CM being shown to overestimate the b.e. by 3–5 MeV. The computed b.e. and r.m.s. radius represent about 50% and 110% of experimental values respectively. The form factorF _ch(q) was computed for 0q ²20 fm^–2; the first-order approximation is a good fit to experimental data, while in the second order diagrams appear that worsen the fit forq ² > >10 fm^–2.The author thanks Professor I. Úlehla for stimulating discussions. The help of dr. J.Hoejí, who calculated a part of higher order diagrams, is gratefully acknowledged.     

Weakly Bound States in Light Hypernuclei

From the viewpoint of critical stability, we discuss the three- and four-body structure of ⁶He, ⁷He, ⁴He, and ⁴H. With the + + N three-body model, ⁶He is found to have a three-layer structure of the matter distribution: core, a skin and neutron halo. Also the level structure of ⁷He with the three-body model of ⁵He + n + n is predicted. This stimulates a new study of neutron-rich and proton-rich hypernuclei. By performing a four-body calculation with both NNN and NNN channels and with both NN and NNN channels, we show that the N-N and -N couplings are very important in critical stability of few-body hypernuclear systems.     

Planck—Wheeler Quantum Foam as White Noise: Metric Diffusion and Congruence Focussing for Fluctuating Spacetime Geometry

It is expected that quantum effects endow spacetime with stochastic properties near the Planck scale as exemplified by random fluctuations of the metric, usually referred to as spacetime foam or geometrodynamics. In this paper, a methodology is presented for incorporating Planck scale stochastic effects and corrections into general relativity within the ADM formalism, by coupling the Riemann 3-metric to white noise. The ADM—Cauchy evolution of a Riemann 3-metric h _ij (t) induced on spacelike hypersurface C(t) can be interpreted within pure general relativity as a smooth geodesic flow in superspace, whose points consist of equivalence classes of 3-metrics. Coupling white noise to h _ij gives Langevin stochastic differential equations for the Cauchy evolution of h _ij, which is now a Brownian motion or diffusion in superspace. A fluctuation h_ij away from h _ij is considered to be related to h _ij by elements of the diffeomorphism group diff(C). Hydrodynamical Fokker—Planck continuity equations are formulated describing the stochastic Cauchy evolution of h _ij as a probability flow. The Cauchy invariant or equilibrium solution gives a stationary probability distribution of fluctuations peaked around the deterministic metric. By selecting a physically viable ansatz for the scale dependent diffusion coefficient, one reproduces the Wheeler uncertainty relation for the metric fluctuations of quantum geometrodynamics. Treating h _ij as a random variable, a non-linear Raychaudhuri—Langevin equation is derived describing the geometro-hydrodynamics of a congruence of fluid or dust matter propagating on the stochastic spacetime. For an initially converging congruence >0 at s the singularity =– at future proper time s=3/||$, which is expected in general relativity, is now smeared out near the Planck scale. Proper time s can be extended indefinitely (s) so that intrinsic metric fluctuations can restore geodesic completeness although the geodesics remain trapped for all time: although a singularity can be removed the collapsing matter still creates a black hole. A Fokker—Planck formulation also gives zero probability that – for s. Essentially, the short distance stochastic corrections to the deterministic equations of general relativity can remove pathologies such as singularities, conjugate points and geodesic incompleteness.     

One-dimensional random walk with self-interaction

A standard random walk on a one-dimensional integer lattice is considered where the probability ofk self-intersections of a path =(0, (1),..., (n) is proportional toe ^–k . It is proven that for <0,n ^–1/3(n) converges to a certain continuous random variable. For >0 the formulas are given for the asymptotic Westerwater velocity of a generic path and for the variance of the fluctuations about the asymptotic motion.     

Scalar mesons in ππ and K¯K scattering

The s-wave pion scattering amplitude is analysed with the aim to clarify the mass spectrum of scalar mesons and to find evidence of lightest glueball. The S-matrix and K¯K coupled channel formalism is used. The existence of scalar mesons S^* and is implied by the data. The production K¯K and the elastic K¯KK¯K coupled amplitudes are predicted from the scattering data. The couplings c f S^* to and K¯K states are determined.     

The puzzle ofKα bound state

Kaonic atom experiments suggest existence of a narrow nuclear¯K bound state and indicate blocking of¯K absorption. This blocking is explained in terms of ₀ resonance and interactions with the nuclear density gradient.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Excition dynamics in the J-aggregates of a carbocyanine dye

We report on the exciton dynamics in the J-aggregating dye 5,5, 6,6-tetrachloro-1,1-diethyl-3,3-di(4-sulfobutyl)-benzimidazolocarbocyanine which is known readily to form J-aggregates, even at room temperature and at a low concentration. We performed a series of time-correlated singlephoton-counting experiments at different emission wavelengths and at different temperatures in the range between 1.5 and 125 K. Additionally, the temperature dependence of the relative fluorescence quantum yield was determined.     

The infinite time limit for the time-dependent Born-Oppenheimer approximation

We analyze the Schrödinger equation , whereH() is the hamiltonian of the molecular system consisting of nuclei with masses proportional to ^–4 and electrons with masses of order 1. Using the Born-Oppenheimer method we construct the leading order asymptotic expansion to the exact solutions of the equation. We show that if the particles interact through smooth potentials decaying suitably as the distance between particles tends to , then the expansion holds uniformly for all timest[0,). By similar analysis one can show validity of the expansion fort(–,0], thus our results hold for scattering theory.The material in this paper is contained in a dissertation submitted to the faculty of VPI & SU in partial fulfillment of the requirements for the Ph.D. degree.     

Double hypernuclei and the Λ-Λ interaction

The binding energy of the double hypernucleus Be¹⁰ analyzed using an -particle model. A relationship is found between B, the binding energy of two -particlcs, and ¯V, the - potential integral. For the experimental value B = 17.5 Me V ¯V varies from 250 to 850 MeV-F³ according to the form of the - potential used.In conclusion, I wish to thank S. N. Kryuchkova for carrying out these calculations on a Minsk-2 electronic computer. I also wish to thank my senior colleague, V. A. Filimonov, for his support in the completion of the present work.     

The interactions¯pp→¯nπ− p at 22·4 GeV/c

The interactions¯pp¯n ^– p are compared with predictions of several models for diffraction dissociation and the validity of these models is tested.     

P-wave charmonium decays into baryon and antibaryon pairs in quark pair creation model

A simple quark pair creation model is introduced to study exclusive decays of _{{c_J}} into baryon-antibaryon pairs. With this simple model, some exclusive decay processes, for example, _{c0} B¯ (B = ,⁰,^-) are investigated and their decay widths are evaluated by inclusion of the properties of outgoing baryons, and the results show that the strengthened decay channels _{{c_J}} ¯(J = 0, 2) are easily understood by considering only the color singlet contribution of P-wave charmonium.     

The coherent K L 0 C → K S 0 C regeneration at high energies

New experimental results on the coherentK _L ⁰ C K _S ⁰ C regeneration in the momentum range 10p30 GeV/c are presented. For the quantity (f ₀–¯f ₀/k (where f₀ and¯f ₀ are theKC and¯K ⁰C forward scattering amplitudes andk is the wave number) we have obtained: arg (f ₀–¯f ₀)/k=–126±14 and ¦(f ₀–¯f ₀/k¦ p ^{–0.62±0.14} These results are well described by a simple Regge pole model including only the (-trajectory exchange in thet-channel with the intercept (0) close to 0.4.Presented at the IV International Symposium on High Energy and Elementary Particle Physics, Warszaw, September 1975.     

A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF