Remarks on the modular operator and local observables

In this paper we give a characterization of the modular group of a von Neumann algebra , with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ₁ and ₂, such that ₁₂, are the mutual commutants, i.e. ₁=₂.An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.Partially supported by C.N.R.     

On the theory of ferromagnetic thin films

As is known, the second approximation in the calculation of the partition function by the traces method of ferromagnetic thin films gives wrong results for the coordination number equal to eight. In order to obtain correct results even for this case, the third order approximation of the partition function is developed and thus the magnetic properties of body-centred cubic iron thin films are studied. The dependence of the Curie temperature on the thickness, for different values of the ratio between the anisotropy constant and the exchange energy between two neighbours, is discussed. A value can be chosen for this ratio such that the thin film becomes ferromagnetic only for a thickness greater than a definite value.

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, . , , (Fe). . , - .

     

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.

     

The distribution of neutron density in the vicinity of a partly inserted black rod in two-group approximation

The neutron density in the vicinity of a black cylindrical rod partly inserted in a bare reactor is calculated and illustrated by a numerical example. The starting point is a two-group diffusion theory approximation. While the dependence of the effect of the rod on the insertion depth can be calculated simply by means of perturbation theory, the question of the neutron density estimate in the vicinity of the rod is considerably more difficult and in some considerations the estimate of the neutron density caused by the presence of the rod is indispensable. The method makes it possible to determine the reactivity value of the rod in dependence on the insertion depth and especially the neutron density deformation in the vicinity of the rod.

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. , . , , . , . [1] . .

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In conclusion the author thanks J. Svato for help in carrying out the numerical calculations.     

Double quantum transitions in free radicals

The observation of double quantum transitions on three kinds of free radicals (DPPH, DPANO, ultramarine) at temperatures of liquid nitrogen is described. Signals having an absorption and emission character were observed in the 12-5 MHz–18 MHz frequency band in the direction parallel to the external magnetic fieldH ₀ and their dependence on different parameters was studied.Bloch equations were solved for two mutually perpendicular high-frequency fields and expressions were found for the components of dynamic susceptibility in theH ₀ direction. The experiments agree with theory.The possibility of using double quantum transitions for measuring relaxation times is discussed.

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(DPPH, DPANO, ) . 12,5MHz–18MHz H ₀, ; . H ₀. . .

     

О СУЩЕСТВОВАНИИ ОТРИ ЦАТЕЛЬНОГО ЯВЛЕНИЯ БАРКГАУЗЕНА

. . , . , . , . coo , 13. 5. 1954 . - .     

Non-equilibrium behavior of sticky colloidal particles: beads,clusters and gels

To understand the non-equilibrium behavior of colloidal particles with short-range attraction, we studied salt-induced aggregation of lysozyme. Optical microscopy revealed four regimes: bicontinuous texture, beads, large aggregates, and transient gelation. The interaction of a metastable liquid-liquid binodal and an ergodic to non-ergodic transition boundary inside the equilibrium crystallization region can explain our findings.     

The electroluminescence of ZnS-Cu,Mn

The brightness waves of ZnS-Cu, Mn phosphor were investigated and it was found that their shape changes from that characteristic for copper-activated phosphors to that characteristic for manganese-activated phosphors as a function of the magnitude of the voltage applied, the length of the pulses and the temperature. In order to explain the results it is assumed that simultaneously with the mechanism of electroluminescence, accepted for ZnS-Cu (ionization of activators; recombination and radiation delayed in phase compared with voltage), there exists an immediate recombination of the Cu activators in the barriers, which is accompanied by radiation in phase with the voltage.

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ZnS-Cu, Mn

ZnS-Cu, Mn. , , , , , , , , . , , ZnS-Cu ( ; , ), : Cu , , .

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In conclusion, the authors thank Dr. M. Trlifaj for valuable discussions and M. Skala for supplying the electroluminescent phosphor of ZnS-Cu, Mn.     

Влияние давления на а бсорбцию галогенидо в серебра. Часть II

AgBr, Agcl AgI — 160°C. AgBr AgCl . AgI .     

Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at r = a and r = b are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a thin shell, (b - a)/a 1. The modified angular frequency for mode ,m can be written as = = ₀ \{ 1 - (GM/a)[2 - ( + 1)/(₀ a)²] where ₀ is the nongravitational frequency. This formula (being independent of m) holds for the magnetic as well as for the electric modes.     

Analysis of special states at the postulated mobility edge in the incommensurate models in 1.d

Scale dependent numerical analysis of the transmission is presented for the novel packeted states and the critical states in two different incommensurate models. Previous work suggests [6] this could be a numerically easy example of studying the mobility edge problematic.     

The crystal structure of meta-zeunerite Cu(UO2)2(AsO4)2⋅8 H2O

The structure of the mineral zeunerite (deposits at Rotava near Kraslice, Ore Mountains) was determined. The tetragonal unit cell, having the dimensionsa=7.10₅Å andc=17.70₄Å, contains two structure units of Cu(UO₂)₂(AsO₄)₂8H₂O. The space group isP4₂/nmc. The distribution of the atoms in the unit cell was determined from the Patterson projectionP(vw) and by means of (F ₀-F _c) synthesis. Meta-Zeunerite has a layer type structure. The sheets [(UO₂)(AsO₄)] are separated by layers containing the cations (Cu(H₂O)₄)²⁺ and molecules of water. The uranium is coordinated octahedrally with six oxygen atoms at distances: U-O₁ 1.94 Å, U-O₂ 1.78 Å, U-O₃₍₄₎ 2.18 Å (4×). The uranyl radical O₁-U-O₂ is linear. In the tetrahedron AsO₄ the interatomic distances are As-O 1.77 Å and the bond angles 102°, 102°, 113° and 113°. Each oxygen atom of the tetrahedron AsO₄ is simultaneously bonded to the uranium atom. The bond angle As-O-U is 137°. The layers [(UO₂)₂(AsO₄)] are bonded together by the cations (Cu(H₂O)₄)²⁺. The distances Cu-O₁ and Cu-O₂ are 2.55 and 2.58Å respectively. The structural changes during hydration and dehydration are explaned.

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- Cu(UO₂)₂(AsO₄)₂8 H₂O

( , ). =7,10₅ Å,=17,70₄ Å Cu(UO₂)₂(AsO₄)₂8 ₂O. P4₂/nmc. P(v w) (F ₀-F _c) . . , [(UO₂)(AsO₄)], , [u(₂)₄]²⁺ . : U-O₁ 1,94 Å, U-O₂ 1,78 Å, U-O₃₍₄₎ 2,18 Å ( ). ₁-U-₂. AsO₄ As- 1,77 Å -102°, 102°, 113° 113°. AsO₄ . As--U 137°. [(UO₂)₂(AsO₄)] [u(₂O)₄]²⁺. u-O₁ 2,55 Å, u-O₂ 2,58 Å. .

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In conclusion the author thanks T. Veselská for assistance in the calculations and workers of the National Museum in Prague, and primarily Dr. ípek, for supplying the sample. The experimental work was carried out at the Department of Physics of the Natural Science Faculty of Komenský University.     

РАДИАЦИОННЫЙ ЗАХВАТ ТЕПЛОВЫХ НЕЙТРОНОВ ЯДРОМ II

, -, Na, Co, Zn, Ag J 20÷1000 keV. Co, Zn, Te J .

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Radiative capture of thermal neutrons on nucleus II

The energies and intensities of gamma rays from the capture of a neutron on Na, Co, Zn, Ag, Te and I nucleus in the 20–1000 keV energy region were measured with a single-crystal, single-channel scintillation spectrometer. New energies of radiative transition were measured when measuring Co, Zn, Te and I nuclei.

     

Paramagnetic resonance of Fe3+ ion in CdWO4 monocrystal

The paramagnetic spectrum of the Fe³⁺ ion in a CdWO₄ monocrystal was measured on a frequency of 9600 kMHz at 290°K. The spin-Hamiltonian of the Fe³⁺ ion was determined and had the form of (1). The constants derived for the spin-Hamiltonian areE/D=0·144±0·002,D=23·8 kMHz.

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Fe³⁺ CdWO₄

Fe³⁺ CdWO₄ 9600 kMHz 290°K. - Fe³⁺ (1), E/D 0,144±0,002 D 23,8 kMHz.

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In conclusion, the authors thank . Bárta and V. Kment from the Society for Chemical and Metallurgical Production in Ústí n/L for producing and supplying the monocrystals and for much valuable advice.     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

The rotation of bloch walls

A Bloch wall has an integral magnetic moment which is due to the spatial distribution of the magnetic moments of the spin. The external magnetic field thus acts on the wall with a torque, which leads to the rotation of the sub-domains and therefore to deformation of the walls. A theory of this rotation is given and from it a microphysical model of the undulatory surface structure in uniaxial ferromagnets is derived. Experiments performed on magnetoplumbite single crystals fully confirm the theoretical assumptions.

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. , , . , . , , .

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Our thanks go to J. Fousek and Z. Málek who by reading this paper contributed greatly to the clarity of its presentation.     

Induced geometry and confinement

A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric _v , an induced metricg _v that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong _v due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given.     

Cyclotron instabilities of a two-component electron plasma

A study is made of instability at frequencies close to the electron cyclotron frequency _B and its multiples, subject to the presence of two different groups of electrons. It is shown that a mixture of hot and cold electrons ( _ph ² _pc ² ) in the region of frequencies s _B, s2 can be unstable with respect to waves of the flute type (k _z=0) with maximum increment _max ( _ph/_pc). _B, if there exists an interval of transversal velocities in whichF/ >0. When the curvature of the magnetic field is taken into account, even waves with _B can be unstable in such a plasma. The effect of spatial inhomogeneity of the hot component on flute-type instability and on two-beam cyclotron instability is also examined.The author extends his thanks to A. B. Mikhajlovskij for his valuable comments and discussions.     

A contribution to the theory of ferromagnetic resonance at high power levels

The instability of spin waves at ferromagnetic resonance is discussed. An equation of the stationary state of spin wavesk0 is derived by means of the quantum theory of spin waves. It is shown when discussing this equation that the concept of the critical uniform precession angle may be obtained when using an approximation which neglects the action of spin wavesk0 backward on their own excitation. We believe we are justified in supposing that, due to this effect, a stable stationary state can exist even above the critical amplitude of uniform precession, given by theories up to now.

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. k0. , , k0 . , , , , .

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In conclusion the author thanks G. A. Smolenskij for enabling him to carry out this work in his laboratory. Thanks also go to the theoretical staff of the Institute of Semi-conductors of Acad. Sci. USSR in Leningrad for valuable discussions, especially to A. I. Anselm, V. L. Gurevic and J. A. Firsov.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.