Graded orthosymplectic geometry and OSp (4;1)-invariant fermionic σ models

A geometry based on the fundamental 4+N-dimensional linear representation of the extended super-de Sitter group OSp(4;N) is considered. For N=1 two OSp(4;1)-invariant fermionic models are discussed.On leave of absence from Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland.     

New quantum deformations ofD=4 conformal algebra

We consider new class of classicalr-matrices forD=4 conformal Lie algebra. These r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel subalgebras. In such a way we generalize the lowest order of known nonstandard quantum deformation ofsl(2) to the Lie algebrasl(4)so(6). As an exercise we interpret nonstandard deformation ofsl(2) as describing quantumD=1 conformal algebra with fundamental mass parameter. Further we describeD=4 conformal bialgebras with deformation parameters equal to the inverse of fundamental masses. It appears that forD=4 the deformation of the Poincaré algebra sector coincides with null plane quantum Poincaré algebra.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Partially supported by the project 5270/95 of the Polish-French Scientific Cooperation.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, 50-204 Wrocaw, Poland.Two of the authors (J.L and M.M) would like to thank the University of Bordeaux I for the hospitality and financial support.     

A generalization of the momentum mapping construction for quaternionic Kähler manifolds

We present a method of reduction of any quaternionic Kähler manifold with isometries to another quaternionic Kähler manifold in which the isometries are divided out. Our method is a generalization of the Marsden-Weinstein construction for symplectic manifolds to the non-symplectic geometry of the quaternionic Kähler case. We compare our results with the known construction for Kähler and hyperKähler manifolds. We also discuss the relevance of our results to the physics of supersymmetric non-linear -models and some applications of the method. In particular, we show that the Wolf spaces can be obtained as theU(1) andSU(2) quotients of quaternionic projective spaceH P(n). We also construct an interesting example of compact riemannianV-manifolds(orbifolds) whose metrics are quaternionic Kähler and not symmetric.On leave from the University of Wrocaw, Wrocaw, Poland     

Energy-momentum complex for nonlinear gravitational Lagrangians in the first-order formalism

It has been recently shown that there is universality of Einstein equations, in the first-order (Palatini) formalism, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations. In this paper the energy-density flow for nonlinear gravitational Lagrangians is investigated in this formalism. It is shown that in the generic case the energy-momentum complex does not depend on the Lagrangian and is in fact equal to the Komar complex, known in the purely metric formalism for the standard linear Hilbert Lagrangian.On leave from the Institute of Theoretical Physics, University of Wrocaw, pl. Maxa Borna 9, 50-204 Wrocaw, Poland     

Hölder continuity of sample paths in Euclidean field theory

Hölder continuity of sample paths of the stochastic process _t (f)=( _t f) (f Y(R ^d–1)) in Euclidean field theory is proved under some assumptions on correlation functions. These assumptions are fulfilled inP()₂ and in theories in which the GHS inequality holds. The continuity index is determined by the condition d(p)|p ₀|²<, whered(p) is the Fourier transform of the two-point function.On leave of absence from Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland     

Classical field theory and analogy between Newton's and Maxwell's equations

A bivertical classical field theory includes the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows one to recognize the formal analogies among Newtonian mechanics and Maxwell's electrodynamics.On leave of absence from University of Wrocaw, Poland. Work partially supported by Polish Committee for Scientific Research K.BN, Grant #2 P302 023 07.     

Three body asymptotic completeness forP(Φ)2 models

We consider weakly coupled even P()₂ models that do not have a two-body bound state, and prove asymptotic completeness on the subspace of states with mass between 3m+a() and 4m–b(), wherea andb are positive functions tending to zero with . The analytic structure of the six point function, integrated over the three incoming momenta, shows only two Landau singular manifolds (plus normal thresholds) associated to three particle processes.Laboratoire associé au Centre National de la Recherche ScientifiqueGroupe de Recherche du C.N.R.S. No. 48     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

Spinors and diffeomorphisms

We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set =H ¹ (M,Z ₂) of inequivalent spin structures and show that it is affine. We argue that in the presence of spinors the gauge group of gravity is a certain double cover ofD(M) which depends on the spin structure. We explicitly compute the action ofD(M) on whenM is a closed Riemann surface; is seen to consist of exactly two orbits, corresponding to even and odd spin structures.On leave of absence from I.F.T., University of Wrocaw, Poland     

On factorization properties of algebraic spinors

We discuss algebraic spinors as elements of a minimal left ideal of the Clifford algebra and observe their factorization property as a column times row in an arbitrary irreducible faithful matrix representation. This allows us to parametrize the set of primitive idempotents and the set of minimal left ideals, and find the dimensionality of the intersection of any minimal left with a minimal right ideal. We propose to generalize Cartan's concept of pure spinors to arbitrary linear spaceR ^{p, q} orC ⁿ .Institute of Theoretical Physics, University of Wrocaw Poland     

Field-emission flicker noise from potassium adsorbed on W(111) bounded and unbounded surface diffusion by spectral analysis

The spectral density functionsW(f) of the field-emission flicker noise of potassium adsorbed on the tungsten (111) region were determined. The analysis in terms of the Gesley-Swanson or the Timm and Van der Ziel model gives surface diffusion energies between 0.54 and 0.31 eV for (average) coverages from 0.15 to 0.38 and diffusion prefactors between 3×10^–1 and 10^–4 cm²/s. The fitting procedures are successful for both bounded and unbounded diffusion though in opposite order of temperature, as expected.On leave from Wrocaw University     

ТЕМПЕРАТУРНАЯ ЗАВИС ИМОСТЬ ТЕРМОЭЛЕКТРОДВИЖУЩ ЕЙ СИЛЫ СЕРОГО ОЛОВА С ПРИМЕСЯМИ КАДМИЯ

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Magnetic anisotropy in thin ferromagnetic films

The magnetic properties of thin ferromagnetic films are studied taking into account the magnetic anisotropy term in the Hamiltonian. In the second approximation equations are obtained for the magnetization of the monatomic layers parallel to the surface of the thin film. From these equations one obtains the Curie temperature, which depends on the thickness of the thin film and the ratio a between the anisotropy constant and the exchange energy between two neighbours. A value can be chosen for such that the thin film becomes ferromagnetic only for a thickness greater than a definite value and in this manner the theoretical results can be fitted to the experimental data. The situation in cobalt thin films is dealt with in particular.

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The author extends his thanks to the research workers of CIFA 1 as well as to Dr. L. Valenta for information on the same subject.     

Application of151Eu Mössbauer spectroscopy to studies of electric field gradients in high-temperature superconductors

The rare-earth site of samples having the compositions (Fe,Cu)Sr₂(Eu,Ce) _n Cu₂O_4+2n+z (n=2 and 3) were studied by¹⁵¹Eu Mössbauer spectroscopy. The results obtained are compared with measurements of EuBa₂Cu₃O_7– (123) and Bi₂Sr₂(Ca_1–yEu_y)Cu₂O_8+E (2212) samples. The full quadrupole Hamiltonian of the 21.5-keV -transition was applied in analyzing the measured spectra. Simultaneous fitting of spectra recorded from crystallites oriented in various directions was used to determine the hyperfine parameters of then= 2 and 3 samples. Two different electric field gradients, not discernible in simple random crystallite measurements, were obtained for then=3 series.     

Hydromagnetic laminar flow of a conducting fluid in an annulus in presence of a radial magnetic field

The object of the present paper is to study the MHD effects on the laminar flow of a viscous, incompressible and conducting fluid in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity in presence of a radial magnetic field. Using finite Hankel transform, solutions for both the unsteady and steady flows under different prescribed pressure gradients have been found out.Notation H a constant characterising the intensity of the magnetic field - p hydrostatic pressure - _e magnetic permeability - coefficient of viscosity - kinematic coefficient of voscosity - conductivity of the medium - density - a radius of the inner cylinder - b radius of the outer cylinder - parameter - s positive root - J (sr) Bessel's function of first kind of ordergl - Y (sr) Bessel's function of second kind of order     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Power law growth for the resistance in the Fibonacci model

Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l ²(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.     

Convexity and concavity of eigenvalue sums

It is well known that(H), the sum of the negative eigenvalues of a Hermitian matrixH, is a concave and increasing function ofH. In contrast to this, we prove that forA nonsingular Hermitian andP positive definite, the functionP(AP)=(P ^1/2 AP ^1/2) is convex and decreasing. Several other results of this nature are also proved.