Approximate calculation of frequencies of localized vibrations

An exact calculation of the frequencies of localized vibrations in a crystal with defects meets with considerable difficulties and therefore only the simplest cases have been calculated [9, 10]. An approximate calculation is confined to computing the frequencies of a system composed of several atoms in the neighbourhood of the defect. The interaction between this system and the other atoms of the lattice, which however are immobile in this approximation, is taken into consideration. Since the analytical estimate of the approximation is very rough, the approximate and exact calculations have been compared for some concrete cases (Fig. 1, 2). It is clear from these calculations that the use of the proposed approximation leads to good results.

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, [9, 10]. , . , , . , (. 1, 2). , .

     

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.     

Bohr's discussion of the fourth uncertainty relation revisited

Bohr's 1930 derivation of the uncertainty relation c ² m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c ² m th, avoiding Treder's 1971 objection.     

Bemerkung über die Reziprozität beim Durchgang des Lichtes Durch Leitfähige Schichten

Zusammenfassung Im vorliegenden Artikel wird die Durchlässigkeit eines beliebigen Systems homogener oder inhomogener Schichten mit beliebiger Leitfähigkeit bei senkrechtem Einfall einer elektromagnetischen Welle untersucht. Es wird bewiesen, da\ das Verhältnis der Durch-lässigkeiten beim Auftreffen der Welle von der einen und von der anderen Seite lediglich von den Leitfähigkeiten der Medien auf beiden Seiten des Systems abhängt. Falls die Leitfähigkeiten beider Medien gleich sind, sind auch die Durchlässigkeiten in beiden Richtungen gleich.

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. , . , .

     

On practical calculations with reflection curves for perfect crystals

The application of the Prins function for practical calculations is rather laborious. In the present article it is shown by analysis of some of the properties of this function that in most experiments with perfect crystals one may use functions of a much simpler form. Such a function is proposed, its use is shown on some examples, a method of simplified calculation of the fundamental constants of the Prins function is given, and finally some numerical examples are added as illustration.

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. , . , , , , .

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These curves will be hereafter called Prins functions.

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The author is greatly indebted to M. Malkovská for the experimental data in Chapter VI. C and to V. Horáková for numerical computations of the integrals in Appendix 2.     

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     

Die magnetische Suszeptibilität der ternären Systeme halbleitender Verbindungen

Zusammenfassung Im vorliegenden Artikel wird der Versuch unternommen, die für die Suszeptibilität der binären Systeme zutreffenden empirischen Beziehungen auf die ternären halbleitenden Systeme auszudehnen. Die Richtigkeit der Erwägungen wird an den Systemen Zn-Cd-Sb, In-Ga-Te und an einigen festen Lösungen anderer halbleitender Verbindungen überprüft. Im Artikel wird weiter gezeigt, daß sich im Falle, wenn sich die Suszeptibilitäten der Komponenten des ternären Systems additiv verhalten, zur Berechnung der molaren Suszeptibilität einer festen Lösung die Mischungsregel verwenden läßt, was im Gegenteil in diesem Falle als Kriterium dienen kann, ob zwei den Erfordernissen der Additivität der Suszeptibilitäten der Bestandteile Genüge leistende Stoffe eine feste Lösung oder ein mehrphasiges System bilden.

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, , . Zn-Cd-Sb, In-Ga-Te . , , , , , , , , , .

     

Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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, (, ) , c. , , , , , . , . , .

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.     

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     

ГАЛЬВАНОМАГНИТНЫЙ Э ФФЕКТ В ОБЛАСТИ ТЕМПЕРАТУРЫ КЮРИ

. - II- . .     

Non-gravitational force effect in general theory of relativity

Equations are derived from the variational principle for a system subjected to an additional non-gravitational force effect, which may be represented by the technical forces imparting to the masses of the system a velocity comparable with the velocity of light and which may change the rest mass of the system, within the framework of the general theory of relativity.

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, , , , , .

     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

On the electroluminescence of powdered zinc sulphide layers

The experimental study of the dependence of the electroluminescence brightness on the voltage confirms the correctness of the mechanism of electroluminescence, based on impact ionization in parts of the crystal where the electric field is concentrated. A study of the photoluminescent and electroluminescent spectra of phosphors containing two activators (copper and an element of rare earth) permits the determination of the magnitude of the volume of the crystal in which electroluminescence occurs. A study of the influence of the stored light sum on the brightness of electroluminescence and a study of the rate of growth of the variable and constant components of electroluminescence point to the fact that the excitation is transferred from the region of field concentration to the whole volume of the crystal.

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, . - , ( ), , . .

     

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.     

The energy of periodic surface structures in ferromagnetism

The periodic domain structures on unfavourably oriented surface layers of ferromagnetic materials were studied both experimentally and theoretically. The connection between the surface structure and the crystallographic orientation of the crystals was confirmed. All the terms contributing to the total energy of the surface layer were calculated. A general solution of the potential problem is given for arbitrary periodic distribution of the charges.

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Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.     

Электродное падение напряжения в конденсированных р азрядах

. , . , .     

Results of three-year systematic measurement of nuclear fall-out

A survey is given of the results of measuring the radioactivity of rain-out from 1. 11. 1956 to 1. 2. 1960 and of fall-out from 1. 11. 1958 to 1. 2. 1960.The temporary cessation of nuclear weapon tests from 1. 11. 1958 became apparent in the second half-year after the cessation (from 1. 5 to 31. 10. 1959) by a decrease in the cumulative activity to 45% of the value for the first half-year (from 1. 11. 1958 to 30. 4. 1959). At the end of 1959 another decrease was apparent.It was shown on the basis of long-term investigation into the activity that the samples of fall-out with greater activity contain relatively very little admixture from earlier nuclear tests so that in the period of a few weeks to months the sets of fission products may be regarded as practically isolated. The exponentn in the relationA=at ^–n is most frequently 1.2 for the period of the first four mounths and for older samples is most oftenn=1.5. The energy of the beta and gamma rays from fall-out was estimated on the basis of absorption measurements. It was shown that the quality of the beta radiation varies with the age of the samples.A brief survey is given of the results of determining the Sr 90 content in fall-out and milk, and of the methods of physical evidence of Sr 90 used.

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1. 11. 1956 1. 2. 1960 1. 11. 1958 1. 2. 1960. 1. 11. 1958 , ( 1. 5. 31. 10. 1959) 45% ( 1. 11. 1958 30. 4. 1959). 1959 . . , , . n A=at ^–n 4 1,2; n=1,5. - - . , - . Sr⁹⁰ . Sr⁹⁰.

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The author thanks Prof. F. Bhounek, member of the Czechoslovak Academy of Sciences, for valuable advice during this work.     

On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL 2(ℝ)+

We consider a random Schrödinger operator onL ²(^v) of the form , {C _i} being a covering of ^v with unit cubes around the sites of ^v and {q _i} i.i.d. random variables with values in [0, 1]. We assume that theq _i's are continuously distributed with bounded densityf(q) and that 0<P(q ₀<1/2)=<1. Then we show that an ergodic mean of the quantity dx|x|²|(exp(itH ))(x)|²t ^–1 vanishes provided =g _E(H ), where is well-localized around the origin andg _E is a positiveC -function with support in (0,E),EE*(, |f|). Our estimate ofE*(, |f|) is such that the set {x ^v |V (x) E*(, |f|)} may contain with probability one an infinite cluster of cubes {C _i} which are nearest neighbours. The proof is based on the technique introduced by Fröhlich and Spencer for the analysis of the Anderson model.Work supported in part by C.N.R. (Italy) and NAVF (Norway)On leave of absence from Instituto di Fisica Università di Roma, Italia     

Schrödinger Operators with Empty Singularly Continuous Spectra

Let H be a semibounded perturbation of the Laplacian H ₀ in L ²( ^d ). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H ₀). If is the exponential function and if e^{– H} is an integral operator we denote the kernel of the difference D = e^{– H} – e^{– H} ₀ by D (x, y), > 0. The singularly continuous spectrum of H is empty if^d dx ^d dy |D(x,y)| (1 + |y|²)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.