ВлИьНИЕ стАцИОНАРНО гО РАсслОЕНИь НА ДВИж УЩИЕсь слОИ В тлЕУЩЕМ РАжРьД Е B Ne

The paper describes a new experimentally found phenomenon of the effect of standing stratification on the parameters of moving striations in the positive column of a glow discharge.

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. . M. Hobaky      

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПОЛЕМ I

, . . . , , . , . , . .

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Betatron oscillations in an accelerator with a general field I

The paper gives a linear theory of equilibrium trajectories in an accelerator with a generalized magnetostatic field, the components of which are defined on a general rotation surface. Equations of motion of the particles in natural coordinates are derived with respect to the change in energy and dissipative force. A system of equilibrium trajectories is found in the general form. Conditions for the field components on the reference surface, necessary for the existence of equilibrium trajectories, for the conservation of their geometric similarities and for maintaining the constancy of the frequencies of the betatron oscillations, are derived. A condition is also derived which must be satisfied by the reference surface in order to conserve constant circular frequency of the particles. It is seen that it is not possible to find a field for an accelerator with an exactly constant circular frequency and with constant frequencies of the betatron oscillation in the relativistic energy region. An ultra-relativistic cyclotron with such properties is realizable.

     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

On the photo-electroluminescence of ZnS-Cu

The influence of weak ultra-violet irradiation on the brightness waves of electroluminescence is investigated for two types of ZnS-Cuphosphors. The observed effects (increase in brightness in the primary peak and its phase shift, the disappearance of the secondary peak) are explained on the basis of present-day conceptions on electroluminescence.

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ZnS-Cu

ZnS-Cu. ( , ) .

     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

The quantum theory of the spontaneous magnetization of ferrimagnetics,anti-ferromagnetics and thin films with arbitrary spin at high temperatures

Using Van Vleck's modification of the Heisenberg theory of ferro-magnetism for substances with arbitrary spin per atom, a generalization of the theory is given for the case of ferrimagnetics, anti-ferromagnetics and thin films with an arbitrary number of sub-lattices and with arbitrary spin per atom. The exchange part of the energy operator is formulated by means of rotated spin operators. The theory contains the quantum-mechanical generalization of non-quantum theories given by Néel and later generalized by Yafet and Kittel. It also contains the theory of thin films proposed recently by the author. The magnetization laws are completely analogous to the relations derived from the theory of molecular fields. The constants of the molecular fields are interpreted by means of exchange integrals. For the special case of spin S=1/2the theory agrees with the results of the work of Vlasov and Imuchametov for ferrimagnetics and anti-ferromagnetics and with the author's for thin films.

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,

, , , . . - , . , . , . . S=1/2 .

     

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II

As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of harmonic oscillators, while the other one is any dynamical system ofn degrees of freedom. Such a problem is of interest both for the realization of holonomic constraints of classical mechanics, and for the freezing of the internal degrees of freedom in molecular collisions. The results of Part I, which referred to the particular case =1, are here extended to the more difficult case >1. For the rate of energy transfer we find exponential estimates of Nekhoroshev's type, namely of the form exp (_*/)^1/a , where is a positive real number giving the size of the involved frequencies, and _* anda are constants. For the particularly relevant constanta we find in generala=1/ however, in the particular case when the frequencies are equal (collision of identical molecules), we finda=1 independently of , as conjectured by Jeans in the year 1903.     

Polarization of photo-luminescence of ZnS: Cu monocrystals

Different models of luminescence centres are discussed on the basis of measurements of the composition of ZnS monocrystal photo-luminescence in different polarizations and temperature dependence of the degree of polarization. Those of the models submitted by Birman, which assume the polarization to be due to the different force of the oscillators for transitions withEc andEc, or models assuming luminescence polarization to be due to the orientation of the luminescence centres, agree with the results of experiments, i.e. the temperature independence of the degree of polarization and the conformable spectral composition of both polarizations. It is also shown that measurements made up to now of the degree of polarization must be taken as orientational as a consequence of the depolarizing influence of the diffused rays of luminescence on its value.

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ZnS: Cu

ZnS , . , . . , , , E E, , . , , - .

     

ДАЛЬНЕЙШИЕ ИССЛЕДОВ АНИЯ ФИЛЬТРА ДВОЙНОГ О ЛУЧЕПРЕЛОМЛЕНИЯ

, 4, (1954), 53. . .     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

On the failure of the time-energy uncertainty principle

We establish, for the quantum system made up of a single free particle, the formula E t(v/c) , where E is the precision to whichE can be ascertained in time t. The measurement can be carried out with zero disturbance inE itself.     

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.     

ВЛИЯНИЕ ОСВЕЩЕНИЯ НА ПРОВОДИМОСТЬ И ФОТОПРОВОДИМОСТЬ З АКИСИ МЕДИ

, Cu₂O - 130–200 °C - . . - . , , , , - , - . - . - .     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.     

Method of moments in analysis of x-ray diffraction lines

A general relation between the moments of the functionsf,g, andh, in the integral equationh(x)=f(y)g(x–y) dy, is derived. This enables any moment of the unknown functionf to be calculated from the moments of the functionsg andh. In particular, if certain assumptions are fulfilled, the moments of the components of the doublet can be calculated with advantage from the moments of the total profile. The statistical significance of the moment characteristics is also emphasized.

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f, g, h h(x)=f(y)g(x–) dy, f g h. , . .

     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

The thickness dependence of the domain structure of magnetoplumbite

The changes in domain structure as a function of the thickness of the crystal are studied on artificial magnetoplumbite crystals. The thickness dependence of the width of the domains is also studied; up to thicknesses of about 10 it follows the theoretical halfpower law. Above 10 the exponent is 0·633. The energy density of the Bloch walls=4·82 erg cm^–2 and the exchange constantA=0·66×10^–6 erg cm^–1 are calculated on the basis of the above measurements.

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. , 10 . 0,633. = =4,82 erg m^–2 =0,66.10^–6 erg cm^–2.

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We thank Z. Málek and V. Janovec for discussions and some remarks.     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld