The one dimensional anderson model with off diagonal disorder: band centre anomaly

We study theE-dependence of the Lyapounov exponent <(E)> of an electron with energyE in the one dimensional Anderson model with off diagonal disorder. In the neighbourhood of the band centre we find for nonzero disorder E)>log^–1 E0 forE0, but all even moments of Re(E) diverge logarithmically. As the probability of Re (E)=0 decreases to zero forE0 we conclude that the electron is always exponentially localised.     

Features of the Sn high-temperature internal friction spectrum

This work measures and studies the high-temperature spectrum of elastic energy absorption in tin. Its features are exhibited and new effects are discovered at 433, 483, and 543 K (peaks A, B, and C), the physical natures of which are explained: peak A by polymorphous --transformation, peak B most likely by stress relaxation caused by this transformation, and peak C by a change in the short-range order in the melt. A connection is also established between the --transformation with the material's aging and purity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 81–86, March, 1987.     

Large-Deviation Principle for One-Dimensional Vector Spin Models with Kac Potentials

We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential J (r)=J(yr), J with compact support. Below the Lebowitz-Penrose critical temperature the limit (mean-field) theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors m s, s any unit vector and m the Curie–Weiss spontaneous magnetization. We prove a large-deviation principle for the associated Gibbs measures. Then we study the system in the limit 0 below the above critical temperature. We prove that the norm of the empirical spin average in blocks of order ^–1 converges to m , uniformly in intervals of order ^–p , for any p 1. We also give a lower bound to the scale on which the change of phase occurs, by showing that the empirical spin average is approximately constant on intervals having length of order ^-1-with (0,1) small enough.     

Instability in degenerate two-photon running wave laser with detuning

The previous stability analysis of the degenerate two-photon running wave laser is extended to the inclusion of detuning between frequencies of cavity and atoms. We derive the analytical equation for the critical pumping and prove analytically that for the special case ofr (/) being unity, there is no Hopf bifurcation instability for the bad cavity. The good cavity case is analysed numerically. The role played by detuning is to raise the critical pumping. In the case ofk (or <K) where there is no Hopf bifurcation instability for the perfect tuning case, the large detuning can give rise to self-pulsing instability.     

Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle

The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants compared to the oscillatory frequency . We conclude that Kramers' low-friction equation is generally valid only for 0<0.01 and has to be modified for 0.01 by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.     

Radiative E1 decay of the1P1 level of charmonium in the sum rules of quantum chromodynamics

An analysis of the radiative decay¹P₁ ¹S₀ + of charmonium is performed by using the sum rules of quantum chromodynamics (QCD). A sum rule that allows for luon power corrections is obtained, and the decay width _c + is computed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 80–84, November, 1991.Finally, the author express thanks to professor R. N. Faustov for valuable advice and useful discussion of the resulting work.     

РАДИАЦИОННЫЙ ЗАХВАТ НЕЙТРОНА ЯДРАМИ Sc,Fe, Cu,Mo, Cd и La

, . 20–1000 keV Sc, Fe, Cu, Mo, Cd La.

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The radiative capture of a neutron on Sc, Fe, Cu, Mo, Cd and La nuclei

The energies and intensities of the transitions of a compound nucleus, produced by the capture of a neutron, were measured by means of a single-crystal scintillation spectrometer. The region of energies 20–1000 keV was measured on Sc, Fe, Cu, Mo, Cd and L a nuclei.

     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Role of Activator and Vacancy Centers in the Decay of the Gamma Scintillators of CsI–Na Crystals

The influence of the concentration of an activator (C _NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C _NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component ₁ = 370 nsec, whereas the components ₁ = 460 nsec and ₂ 2 sec are associated with VRC. The reduction of ₁ from 770 to 560 nsec with an increase in C _NaI from 2·10^–3 to 3·10^–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.     

Computational study of propagating fronts in a Lattice-gas model

Velocities and other features of propagating fronts in the lattice-gas model analyzed by Bramsonet al. are computed by Monte Carlo simulation. The propagation velocity() is found to converge slowly to its asymptotic dependence on the exchange-rate parameter. The number density of occupied sites in the interaction zone (extending from the forwardmost occupied to the rearmost unoccupied site) appears to converge to 2/3 for large. Spatial profiles of site occupancy and interface number density for finite are compared to the profiles originally computed by Fisher using the differential equation obeyed in the large- limit. Several significant features inferred from the computations have not yet been explained analytically.     

On the spectrum of the Rayleigh piston

We make a rigorous study of the spectrum of the Rayleigh piston. Our main results are that one is dealing with a trace-class perturbation for all values of the mass ratio y between test particles and heat bath particles and that apart from the ground state the discrete spectrum is empty for y sufficiently near 1. We also show that the so-called Lorentz limit ( ) is mathematically well defined and derive a qualitative statement on the discrete spectrum of the scattering operator for 1.     

Nonlinear two-photon interaction in a strong magnetic field

Sections of nonlinear photon-photon scattering processes and merger of photons in the nucleus (Ze) (Ze) in a strong magnetic field are computed by using a developed two-dimensional formalism. Closed expressions are obtained for the sections with a graphical illustration of the results and they are compared with the case of no external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 16–19, June, 1988.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

The magnetic moment of103Ru

The nuclear magnetic moment of¹⁰³Ru has been determined using the technique of low-temperature nuclear orientation on¹⁰³Ru as a dilute impurity in Fe. The Fe lattice was cooled to 1.7 mK using a PrNi₅ enhanced nuclear demagnetisation stage precooled with a³He–⁴He dilution refrigerator. The¹⁰³RuFe system was observed to have a long nuclear spin-lattice relaxation time, but analysis of the relaxation indicates that the¹⁰³Ru nuclei are close to thermal equilibrium with the Fe lattice at times>200 min after demagnetising. From the near thermal equilibrium anisotropy of the 497 keV -ray in¹⁰³Rh we have deduced the nuclear magnetic moment as |(¹⁰³Ru)|=0.18(2)_N. This value is almost independent of the choice of spinI=3/2 or 5/2 for the nucleus, but is only consistent with systematics ifI(¹⁰³Ru)=3/2 and <0. UsingI=3/2 we obtain the E2/M1 mixing ratio of the 497 keV -ray as =–0.42(4). The sign of the anisotropy of the 610 keV -ray from the 650 keV level in¹⁰³Rh is only consistent with an allowed -decay to the state ifI(650 keV,¹⁰³Rh)=5/2. The E2/M1 mixing ratio of the 610 keV -ray is then =+0.15(3) or +60( _–40 ⁺ ), <–80. From the initial rise in -ray anisotropy following demagnetisation we determine the Korringa constant for¹⁰³RuFe to beC=5.7(5) K·s.     

Structure investigations on the hot-working behaviour of steel

Structure changes occurring in hot-deformation of the austenite of steel, the - phase transformation of which takes place above room temperature, cannot directly be studied with quenched specimens. However, within certain limits a microstructure characterization is possible by means of investigation of carefully selected model alloys and/or by analysis of the microstructure inheritance associated with a martensitic - transition of the hot-worked austenite. Application of both procedures is demonstrated with results which were obtained in investigations of the hot-working behaviour of low-alloy spring steel and an Fe-Ni-C model alloy.     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.     

Experimental study of the albedo of a beam of γ rays produced by ultrarelativistic electrons

A study has been carried out of the spectral dependence of -radiation scattered from targets irradiated with beams of rays produced by relativistic electrons in crystals. It is shown that the change in the spectral composition of the beam of rays incident on the target changes considerably the spectral properties of the scattered radiation. The spectra of the scattered radiation are studied as a function of the thickness and atomic number of the scatterer. It is shown that the atomic number of the scattering material can be determined from the ratio of the spectral components of the scattered radiation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 106–119, June, 1991.     

Structural stability properties of friedman cosmology

A dynamical system with Robertson-Walker symmetries and the equation of the statep=, 01, considered both as a conservative and nonconservative system, is studied with respect to its structural stability properties. Different cases are shown and analyzed on the phase space (x=R ^D , y=x).     

Recent experiments in novel nuclear excitations at the BNL AGS

Recent experimental work at the AGS dealing with unusual nuclear excitations is summarized. Three examples are given: the deexcitation of A hypernuclei by transitions, the production of A hypernuclei by the (⁺, K⁺) reaction, and the search for -nuclear excitations. The status of each field and the implications of the research for nuclear theory are discussed.Invited talk to the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia, September 5–10, 1988.