Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory

With aC*-algebra with unit andgG _g a homomorphic map of a groupG into the automorphism group ofG, the central measure of a state of is invariant under the action ofG (in the state space of ) iff is -invariant. Furthermore if the pair { ,G} is asymptotically abelian, is ergodic iff is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on , the associated covariant representations of { , } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

On the domains of generalized operators

The domains of generalized operatorsT: _–+ on rigged Hilbert spaces _– H ₊ are investigated. We introduce an equivalence relation for operators with different domains. Arguments are given for taking ₊ to be the weak quasi-completion of _– and for _– to be Mackey quasi-complete. For domains of closed symmetric Hilbert space operators we give a representation for ₊ and provide certain elements in the equivalence class of the corresponding operator.     

Bianchi and Weyl equations as sufficient equations for Einstein spaces

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinor _ABCD considered arbitrary and with the background space unspecified, ^EA _EBCD=0; (+12) _ABCD –6(AB ^EF ( _CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinor _ABCD has to be the Weyl spinor of this space.     

Parametric dependence of the properties of pulsed-laser-deposited diamond-like carbon films

The properties of Pulsed-Laser-Deposited Diamond-Like Carbon (PLD DLC) films are studied as functions of the power density and the wavelength of the laser beam, and the incident angle of the beam relative to the normal of the target surface. All the films have a similar structure consisting of graphite particulates embedded in a continuous matrix, so the macroscopic performance of the films is determined by the overall contributions of the particulates and the matrix. The use of higher, shorter, or larger leads to an enhancement of the diamond-like characteristics and a simultaneous increase of the particulate density. These two effects give opposite contributions to the electrical conductivity _R, leading to the following results. (i) _R drops with increasing in the low range (region I) due to the stronger diamond-like nature of the matrix, but increases sharply after has exceeded a threshold _min as a result of the rapid increase in particulate density. (ii) In region I, the use of shorter or larger leads to a more diamond-like matrix, and this overwhelms the degradation effect caused by the slight increase in particulate density. The samples thus become more insulating. In the high region (region II), however, the use of shorter or larger gives rise to higher particulate density, thereby increasing the electrical conductivity.     

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.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Electronic absorption and emission spectral data and fluorescence quantum yields of bridgedp-oligophenylenes,bi- to deciphenyls,and related furans and carbazoles

Absorption and fluorescence emission spectral data, as well as fluorescence quantum yields (_f), were determined for 41p-oligophenylene compounds containing 2–6, 8, and 10 benzene rings. Of 29 compounds containing carbon-bridged rings (fluorenes), 28 were dialkylated on each bridge for improved solubility and photostability. Absorption maxima for oligophenylenes were observed at wavelengths as long as 366 nm, emission maxima to 437 nm, and molar extinction coefficients () as large as 153,000 L/mol-cm; all three exceeded predicted maximum values for the corresponding unbridged oligophenylenes. The substitution of furan for benzene or carbazole for a fluorene (two examples each) bathochromically shifted absorption and emission maxima. Dialkylated carbon bridges bathochromically shifted absorption and emission maxima, and lowered _f in biphenyl and in one terphenyl analogue, but appeared to cause no diminution of _f in higher oligophenylenes. Bis(2-methoxyethyl) substitution on the bridges, incorporated to provide solubility in polar solvents, lowered _f in all examples. Tertiary alkyl substituents on terminal rings bathochromically shifted the absorption and emission maxima and generally increased _f. The loose bolt effect, which lowers _f in mononuclear substituted benzenes, may operate in 9,9-dialkylfluorenes, but not in 2,7-di-t-butylfluorene or in higher oligophenylenes. Cyclic ether and methoxy substituents as auxofluors on terminal rings generally bathochromically shifted absorption and emission maxima and increased and _f. Cyano substituents bathochromically shifted absorption and emission maxima, and increased , but lowered _f slightly.     

Phi-symmetric effect algebras

The notion of a Sasaki projectionon an orthomodular lattice is generalized to a mapping : E × E E, where E is an effect algebra. If E is lattice ordered and is symmetric, then E is called a -symmetric effect algebra.This paper launches a study of such effect algebras. In particular, it is shown that every interval effect algebra with a lattice-ordered ambient group is -symmetric, and its group is the one constructed by Ravindran in his proof that every effect algebra that has the Riesz decomposition property is an interval algebra. It is shown that the doubling construction introduced in the paper is connected to the conditional event algebrasof Goodman, Nguyen, and Walker.     

Currents and Super-Operator Product Expansionsof N = 4 Super-W Algebra

The currents and the super-operators product expansions of theN = 4 super-Walgebra are obtained. The generators of this extended conformal algebra consistof the stress-tensor superfield J and the primary superfields _±v ^q of integer orhalf-integer conformal weight and Cartan–Weylcharge q. The algorithm forderiving the N = 4 super-W algebra is given for particular cases. Explicit formsof the operator product algebra for different values of are given.     

More surprises in the general theory of lattice systems

I use Israel's methods to prove new theorems of ubiquitous pathology for classical and quantum lattice systems. The main result is the following: Let be any interaction and be any translation-invariant equilibrium state for (extremal or not). Then there exists a sequence { _k } of interactions converging to , having extremal (or even unique) translation-invariant equilibrium states _k , such that { _k } converges to . In certain situations the perturbations _k – can be chosen to lie in a cone of antiferromagnetic pair interactions. I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r ² interaction (Thouless effect).     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

Treatment of droplike clusters in nucleation theory using Reiss's method

The expression of the correction factor in nucleation theory is derived by extending the method Reiss used recently. is the factor appearing in the number of critical nuclei (formed as a vapor condenses into liquid drops) as a correction to the conventional theory. It is shown that=p _l / _g /kT, wherep _l is the pressure of the liquid phase inside the drop, _g , is the volume per molecule in the vapor phase,k is the Boltzmann constant, andT is the absolute temperature. The difference between this and Reiss's expression isp _l , which replaces hisp _g (the vapor pressure in equilibrium with the drop). The derived in this paper is compatible with the expression= _g / _l ( _l is the molecular volume in the liquid phase) previously proposed by the present author.     

Concept of time in the general law of thermodynamics as the basis of the thermodynamics of the nonequilibrium state

A mathematical formulation is proposed for the general law of thermodynamics in the form of relations defining the concept of thermodynamic time and the criterion of stable equilibrium. It is hypothesized that an implicit function F(, , , , ... ⁽ⁿ⁾)=0 associates the thermodynamic time and the potential of the nonequilibrium state. Partial solutions of a general form are also obtained for the trajectories of a nonequilibrium process, characterized by the presence of only one independent variable, i.e., =(⁽ⁿ⁾).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 49–54, August, 1989.     

Interfacial free energies and solute diffusivities from data on Ostwald ripening

Using recent theoretical modifications of the kinetic constants characterizing Ostwald ripening, it is demonstrated that accurate values of the interfacial free energy, , and solute diffusivities, D, can be obtained from experimental data when the kinetics of particle growth are measured in conjunction with independent measurements of either the decrease of the matrix supersaturation or the increase in volume fraction with aging time. The accuracy of is limited only by the assumption that the matrix phase is an ideal solid solution, and is effectively independent of the influence of equilibrium volume fraction, _e, on the kinetics of coarsening. Analyses of the available data on the coarsening of -type (Ni₃X) precipitates in binary Ni–Al, Ni–Si and Ni–Ti alloys yield values of =6.9±0.3, 10.2±3.0 and 13.0 mJ/m², respectively, assuming ideal solution thermodynamics; a more realistic thermodynamic model for the Ni–Al solid solution raises the value of in Ni–Al alloys to 8.1±0.2 mJ/m². Proportional increases probably obtain in the other two alloys. The accuracy with which D can be evaluated from comparable data depends theoretically on _e. However, analyses of the same data yield values of D in very good agreement with the results of conventional diffusion experiments. This is consistent with the absence of an effect of _e on the kinetics of Ostwald ripening in these alloys over the ranges of _e investigated.     

Streuung spinpolarisierter Elektronen an Au(110)

Using the the spin modulated polarized electron gun based on photoemission from positive affinity GaAs the intensityI(E, , ) and asymmetry (E, , ) are measured in LEED from Au(110). The asymmetry is compared with the polarizationS(E, , ) which N. Müller obtained with a Mott detector after scattering an unpolarized electron beam from the same crystal. There is excellent agreement for the (00) beams, if the scattering plane is a mirror symmetry plane of the crystal (=0°, =90°). From the differences for the (00) and (11) beams at =35° and the (01/2) beam at =90° conditions for possible models for the reconstructed Au(110)–(1×2) surface may be derived.

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Die vorliegende Arbeit ist ein Auszug aus [1]

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Neue Addresse ab 1. Oktober 1980: B. Reihl, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA     

On the correlation for Kac-like models in the convex case

The aim of this paper is to stu the behavior asm tends to of a family of measures exp[- ^(m)(x)]dx ^(m) on ^m , where ^(m) is a potential on ^m which is a perturbation in a suitable sense of the harmonic potential _j x _j ² .     

Supersymmetric path integrals applied to the transmission of a mesoscopic ring

The average transmission probability of a one-dimensional mesoscopic ring is calculated for arbitrary disorder strength. With increasing disorder the dependence on the magnetic flux changes from ₀ to ₀/2 periodicity. A supersymmetric method is used for the calculation which leads to the quantum mechanics in super-space of an anharmonic oscillator with hyperbolic symmetry. As a byproduct the transmission of a mesoscopic wire is obtained. The inverse of the localization length is given by the lowest eigenvalue of the oscillator.Research performed within the program of Sonderforschungsbereich 341 Köln-Aachen-Jülich     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

Phantom scalar fields in five-dimensional Kaluza-Klein theory

The existence of a so-called "phantom" scalar field in some Riemannian spaceV ₄, i.e., a field in which the effective energy momentum tensorT ^(sf) vanishes in the five-dimensional Kaluza-Klein theory, is investigated by means of the integrability conditions for relations of the form _;;=k_,,+bg found in [6]. Phantom fields are found in homogeneous isotropic cosmological models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–56, February, 1996.