Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 3

We continue the analysis of the conjugate equation for the generating function of a Gibbs random point field corresponding to a stationary solution of the classical BBGKY hierarchy. This equation was established and partially investigated in the preceding papers under the same title. In the present paper we reduce a general theorem about the form of solutions of the conjugate equation to a statement which relates to a special case where the interacting particles constitute a quasi—one dimensional configuration.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.     

Magnetic anisotropy in thin ferromagnetic films

The magnetic properties of thin ferromagnetic films are studied taking into account the magnetic anisotropy term in the Hamiltonian. In the second approximation equations are obtained for the magnetization of the monatomic layers parallel to the surface of the thin film. From these equations one obtains the Curie temperature, which depends on the thickness of the thin film and the ratio a between the anisotropy constant and the exchange energy between two neighbours. A value can be chosen for such that the thin film becomes ferromagnetic only for a thickness greater than a definite value and in this manner the theoretical results can be fitted to the experimental data. The situation in cobalt thin films is dealt with in particular.

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. , . , . , , - , . , , .

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The author extends his thanks to the research workers of CIFA 1 as well as to Dr. L. Valenta for information on the same subject.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

The diffusion and non-radiative transfer of excitation energy in molecular crystals containing foreign molecules

A study is made of the non-radiative transfer and diffusion of excitation energy in molecular crystals containing foreign molecules and its influence on the luminescent properties of these crystals.

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,

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On the ferromagnetism of thin films

In this paper the magnetic properties of ferromagnetic thin layers are studied by calculating the partition function for the magnetic system inKirkwood's approximation of the second order. The results obtained for the Curie temperature and the magnetization are in somewhat better agreement with the experiment than those obtained by Valenta.

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. , , .

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The author extends his thanks to the group of research workers who performed the numerical calculation of the Curie temperatures on the computer CIFA 1, as well as gratitude to Dr. l. Valenta for so kindly supplying information on the results of his investigations on the same subject.     

On pseudoparticle solutions in Yang's theory of gravity

Within the framework of differential geometry, Yang's parallel-displacement gauge theory is considered with respect to pure gravitational fields. In afour-dimensional Riemannian manifold it is shown that thedouble self-dual solutions obey Einstein's vacuum equations with the cosmological term, whereas the doubleanti-self-dual configurations satisfy the Rainich conditions of Wheeler'sgeometrodynamics. Conformal methods reveal that the gravitational analog of the instanton or pseudoparticle solution of Yang-Mills theory was already known to Riemann.     

The quantum theory of multipole radiation in a dielectric

The potentials of an electromagnetic field of multipoles in a dielectric, which is realized by a dielectric sphere having a perfectly conducting surface, are derived. The diagonal values of the energy for thez component of the angular momentum and the square of the angular momentum of the field are determined and also the ratio between thez component of the angular momentum and the energy and the ratio between the square of the angular momentum and the square of the energy. It is shown that the total angular momentum can be divided in the usual way into orbital and spin parts but that these parts cannot be interpreted as the orbital and spin angular momentum because their eigenvalues cannot be the eigenvalues of any operator of infinitesimal rotation. In the commutation rules of a multipole field the vector character of the field is to a certain extent suppressed and the spin of the photon in a state with a certain value of the energy, parityz component of the angular momentum and the square of the angular momentum is not defined.

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, . ,z— , , z— . , , , , , - . , ,z— .

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In conclusion the author thanks Dr. . Muziká for directing the work, F. Samek for valuable remarks and discussion and J. Kvasnica for help in preparing the paper for publication and for adding a number of remarks.     

Configuration mixing and deviations of magnetic moments from Schmidt lines

Deviations of nuclear magnetic moments of oddA nuclei from the Schmidt lines are explained by configuration mixing. The general results obtained are applied to several nuclei and the magnitudes of the admixture coefficients necessary to explain the deviations are estimated. The results show that the deviations can be successfully explained only for those nuclei, in which possible configuration admixtures give contributions to the magnetic moment linear in the admixture coefficient.

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A . , . , , , .

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This work was done as a diploma thesis at the Faculty of Technical and Nuclear Physics, Technical University, Prague.

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In conclusion I want to thank Dr. L. Trlifaj for suggesting this subject and for his guidance in its realization.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

Quantum mechanics and the direction of time

In recent papers the authors have discussed the dynamical properties of large Poincaré systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. We show that this Poincaré catastrophe can be eliminated by a natural time ordering of the dynamical states. We obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that this time ordering can be performed in an extended Hilbert space. In general, we need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.     

Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.

     

The electroluminescence op ZnS-Cu single crystals excited with pulses of alternating polarity

The brightness waves of electroluminescence of ZnS—Cu were measured for the case of excitation with rectangular pulses as a function of the amplitude of the pulses and the temperature. A concrete model is proposed for electronic processes in barriers in ZnS crystals, the consequences of which for the decay of electroluminescence are in agreement with measurements.

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ZnS-Cu,

e ZnS-Cu . ZnS-Cu, .

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In conclusion the author thanks M. Trlifaj for valuable remarks and discussions, Z. Vojta and E. Rechziegel for constructing an important part of the apparatus and F. Karel for the electroluminescent crystals.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНК ИХ СЛОЕВ. I. ЧАСТЬ

- - , - . - . -, - [6]. 1956 . , .     

Химическая сенсиБил изация фотографичес кой эмульсии

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Chemical sensiblilisation of photographic emulsion

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, 7. V. 1953 .     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Singleton Field Theory and Flato–Frønsdal Dipole Equation

We study solutions of the equations ( - ) = 0 and ( - )² = 0 in global coordinates on the covering space CAdS _d of the d-dimensional Anti de-Sitter space subject to various boundary conditions and their connection to the unitary irreducible representations of (d-1,2). The vanishing flux boundary conditions at spatial infinity lead to the standard quantization scheme for CAdS _d in which solutions of the second- and the fourth-order equations are equivalent. To include fields realizing the singleton unitary representation in the bulk of CAdS _d one has to relax the boundary conditions thus allowing for the nontrivial space of solutions of the dipole equation known as the Gupta–Bleuler triplet. We obtain explicit expressions for the modes of the Gupta–Bleuler triplet and the corresponding two-point function. To avoid negative-energy states one must also introduce an additional constraint in the space of solutions of the dipole equation.     

Струи паров материал ов электродов нри кратковременном электрическом разря де с Большой силой тока

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The vapour jets of electrode material of a short-time high-intensity electric discharge

The velocity of vapours from electrodes and the values of the electric gradient of the channel were measured. An explanation is given of the dependence of the discharge rate of the vapours on the electrode material and the thermal origin of the jets is confirmed. The validity of the results is shown for the case of a different experimental arrangement, or the formation of other types of discharges on electrodes.