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.     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

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= –.     

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.     

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.     

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.     

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     

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.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

ВЛИЯНИЕ СОДЕРЖАНИЯ К ИСЛОРОДА НА ЭЛЕКТРИЧЕСКИЕ И ТЕ РМОЭЛЕКТРИЧЕСКИЕ СВОЙСТВА ТРОЙНОЙ СИС ТЕМЫ Вi2Те3−x Sе x

, Bi₂Te_3–x Se _x . , , . , , . .

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Influence of oxygen content on electric and thermoelectric properties of ternary system Bi₂Te_3–x Se _x

A study is made of the influence of oxygen, contained in the semi-conducting system Bi₂Te_3–x Sé _x , on the electric and thermoelectric properties. It is shown that the addition of oxygen to the prepared samples Bi₂Te_2.4Se_0.6 causes a decrease in electric conductivity while the thermoelectric force remains unchanged. This influence is connected with a decrease in the mobility of the electrons but their concentration is not influenced by the presence of oxygen. Conclusions are reached as to the influence of oxygen on the efficiency of the conversion of thermal energy into electric energy and vice versa.

     

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.     

Five-dimensional null-cone structure of big bang singularity

Firedmann model of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five dimensional Minkowski spaceM ⁵ is globally rigid: if F() and F() are isometric imbeddings inM ⁵ there is a motion of M⁵ such that F= °f. The big bang singularity is the vertex of a null half-cone inM ⁵. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.     

A complete proof of the Feigenbaum conjectures

The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point ^* for this map is found. The usual renormalization group doubling operatorN acts on this function ^* simply by multiplication of with the universal Feigenbaum ratio ^*= 4.669201..., i.e., (N ^*(,t)= ^*( ^* ,t). Therefore, the one-parameter family of functions, ^* , ^* (t)=( ^*(,t), is invariant underN. In particular, the function ₀ ^* is the Feigenbaum fixed point ofN, while ^* represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.     

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.     

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.     

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).     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

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.     

gl q (n) and quantum monodromy

A generalized Toda lattice based on gl(n) is considered. The Poisson brackets are expressed in terms of a Lax connection, L=–() and a classical r-matrix, {₁,₂}=[r,₁+₂}. The essential point is that the local lattice transfer matrix is taken to be the ordinary exponential, T=e; this assures the intepretation of the local and the global transfer matrices in terms of monodromy, which is not true of the T-matrix used for the sl(n) Toda lattice. To relate this exponential transfer matrix to the more manageable and traditional factorized form, it is necessary to make specific assumptions about the equal time operator product expansions. The simplest possible assumptions lead to an equivalent, factorized expression for T, in terms of operators in (an extension of) the enveloping algebra of gl(n). Restricted to sl(n), and to multiplicity-free representations, these operators satisfy the commutation relations of sl _q (n), which provides a very simple injection of sl _q (n) into the enveloping algebra of sl(n). A deformed coproduct, similar in form to the familiar coproduct on sl _q (n), turns gl(n) into a deformed Hopf algebra gl _q (n). It contains sl _q (n) as a subalgebra, but not as a sub-Hopf algebra.