The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

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.     

The (n, α) reaction measurements on143Nd and180Hf with thermal neutrons

The thermal neutron cross sections for several-transitions of the¹⁴³Nd(n,) reaction have been measured using a semiconductor surface barrier telescope. The¹⁴³Nd(n, ) reaction has been observed. The¹⁸⁰Hf(n,) cross section estimation is given.The authors are in lebted to Mrs. M.Pospíilová, Mr. J.Baura and Mr. J.Novotný for their assistance during the experiment and Dr. K.Konený for the neutron capture gamma rays analysis.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

The stability and instability of relativistic matter

We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namelyp ²/2m is replaced by (p ² c ²+m ² c ⁴)^1/2–mc ². The electrons are allowed to haveq spin states (q=2 in nature). For one electron and one nucleus instability occurs ifz>2/, wherez is the nuclear charge and is the fine structure constant. We prove that stability occurs in the many-body case ifz2/ and <1/(47q). For smallz, a better bound on is also given. In the other direction we show that there is a critical _c (no greater than 128/15) such that if > _c then instability always occurs forall positivez (not necessarily integral) when the number of nuclei is large enough. Several other results of a technical nature are also given such as localization estimates and bounds for the relativistic kinetic energy.Work partially supported by U.S. National Science Foundation grant PHY-85-15288-A02The author thanks the Institute for Advanced Study for its hospitality and the U.S. National Science Foundation for support under grant DMS-8601978     

Experimental study of the neutron emission mechanisms in a Filippov-type plasma focus device

The results of an experimental investigation of neutron emission characteristics in the Filippov-type plasma focus facility Dena (90 kJ, 25 kV, 288 µF) with D₂ + %1 Kr as working gas are presented. From the experimental results, one can conclude that both thermonuclear and nonthermonuclear mechanisms are always present in neutron production, but their contributions to the total neutron yield are strongly dependent on the initial pressure and discharge voltage. It has been found that at constant discharge voltages and low pressures the beam—target interaction mechanism plays an important role in the neutron production and with increasing the pressure, its role decreases and the importance of thermonuclear mechanism increases. Also at constant pressures, the contribution of beam—target interaction mechanism in neutron production decreases with increasing the discharge energy. The value of the index in the empirical neutron yield scaling law Y_n I E^/2 was found to be about 3.82.     

Improved bounds for the transition temperature of directed polymers in a finite-dimensional random medium

We consider the problem of directed polymers in a random medium of a finitedimensional lattice. In the high-temperature phase of this system it is known that the annealed and quenched free energies coincide. Upper bounds on the transition temperature to a low-temperature phase had previously been obtained by calculating the first two moments Z and Z² of the partition function. We improve these bounds by estimating noninteger moments Z for 1<<2.     

Calculation of hyperfine interactions measured by magnetic decoupling in oxygen ions

Magnetic hyperfine interactions in highly stripped oxygen ions recoiling in vacuum have been measured with perturbed angular correlations. The second excited state of¹⁶O(I =3^–,E _X=6.13 MeV, =26.6 psec, |g|=0.55) was produced with the nuclear reactions¹⁹F(p,)¹⁶O and¹⁶O(,)¹⁶O and the angular correlation of the -rays observed in coincidence with particles emitted at 180°. Five recoil velocities between 1.0 and 3.3% c produced average ion charge states from 2.1 to 5.5. The perturbation of the angular correlation and hence the decoupling of the hyperfine interactions was observed as a function of an external axial magnetic field varied between 0 and 33 kG. The perturbation is expected to arise primarily from hyperfine interactions of unpaired 1s electrons with smaller contributions from 2s electrons and other configurations. The maximum external field was strong enough to decouple all hyperfine interactions except that of the 1s electrons. The decoupling curves obtained were successfully fitted by calculations using the hyperfine interactions of the pertinent atomic Hartree-Fock-Slater orbitals.Supported in part by the National Science Foundation.     

The Sine-Gordon field theory model at α2=8π, the non-superrenormalizable theory

We study the Sine-Gordon field theory at ²=8. We prove that the theory is renormalizable but not superrenormalizable and we show how the perturbative renormalization procedure works in this case where the interaction is not polynomial. To go beyond the perturbative results we investigate the -functional equation for this theory and discuss in what sense at ²=8 the theory is lacking the asymptotic freedom and how it is asymptotic free for ²<8 in a appropriate region of the coupling constants.     

On the global behaviour of symmetric Skyrmions

It is shown that the chiral angle, (r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, (r) is strictly convex or concave. As r, (r) and (r) approach their limit values at the rate Or ^- for any (0,2).     

Almost periodic Jacobi matrices associated with Julia sets for polynomials

Let be the Jacobi matrix associated with polynomialT(z) of degreeN2. The spectrum of is the Julia set associated withT(z) which in many cases is a Cantor set. Let ⁽¹⁾ denote the result of omitting the first row and column ofJ. Then it is shown that the spectrum of ⁽¹⁾ may be purely discrete.It is also shown that forT(z)= ^NC_N(z/) for > , whereC _N is a Chebychev polynomial the coefficients of and ⁽¹⁾ are limit periodic extending the work of Bellissard, Bessis, and Moussa (Phys. Rev. Lett.49, 701–704 (1982)).Supported in part by N.S.F. grant DMS-8401609Supported in part by N.S.F. grant MCS-8203325     

A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model

LetH=–+V onl ²(), whereV(x),x, are i.i.d.r.v.'s with common probability distributionv. Leth(t)=e ^–itv dv(v) and letk(E) be the integrated density of states. It is proven: (i) Ifh isn-times differentiable withh ^(j)(t)=O((1+|t|)^–) for some >0,j=0, 1, ...,n, thenk(E) is aC ⁿ function. In particular, ifv has compact support andh(t)=O((1+|t|)^–) with >0, thenk(E) isC . This allowsv to be singular continuous. (ii) Ifh(t)=O(e ^–|t|) for some >0 thenk(E) is analytic in a strip about the real axis.The proof uses the supersymmetric replica trick to rewrite the averaged Green's function as a two-point function of a one-dimensional supersymmetric field theory which is studied by the transfer matrix method.Research partially supported by the NSF under grant MC-8301889     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Quadratic form techniques and the Balslev-Combes theorem

We extend the theorem of Balslev and Combes on the absence of singular continuous spectrum to a class of interactions includingr ^–(3/2<2) local potentials. In addition, we note that the theory of sectorial operators allows a simplification of their proof and allows one to push the cuts through angles larger than the /2 restriction employed by Balslev-Combes.A. Sloan Foundation Fellow.     

Upper bounds onT c for one-dimensional Ising systems

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n interactions, where 1<2. In particular for the often studied case of =2 we have an upper bound onT _c which is less than theT _c found by a number of approximation techniques. Also for the case where is small, such as =1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.     

On the homology of lattice vibrations of alkali metals

Investigations of the dependence of lattice vibrations of alkali metals on their interatomic distance,r reveal that they satisfy an empirical relation,Mv ² r =(q), a constant which depends on, with q=2·48 ± 0·19 at all wave vectors and hence are homologous. It is shown that the observed crossover of [00] branches of lithium is not an anomalous property, but only manifests itself in alkali metals with smaller interatomic distance due to small variations of . The role played by interatomic distance which is closely related to that of the electron gas constantC in producing a crossover and a possible reason for the observed homology are discussed.The authors are grateful to Professor B. Sharan and Mr. S. B. Rajendraprasad for many valuable and stimulating discussions. One of the authors (M. S.) is greatly indebted to Professor D. M. Sen, principal, and Professor L. V. Sud of Regional Engineering College, Kurukshetra, for granting him study leave.     

TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.