The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

---

. . . , , .

---

---

The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

---

In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Bunching phenomena during electron injection into the betatron II. Theory of starting conditions

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments described in [1]. The bunching is treated as a small perturbation of the stationary beam.The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance.Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in reasonably good agreement with the experiments. Such agreement may be considered as further verification of the statement made in [1] that the amplification of the disturbances is caused by the negative mass instability mechanism.

---

, .

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

     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

The distribution of dislocations in silicon iron single-crystals grown from the melt

The distribution of dislocations in a crystal of an Fe-4.2% Si alloy prepared from the melt is studied microscopically and, by X-ray diffraction after rendering them visible by anodic dissolving. The dislocations are also studied inside the crystal by successively grinding the surface. The density of the dislocations inside the blocks is determined by calculation from microphotos, the density of the dislocations forming the boundaries between the blocks by measuring the angles between the lattices of neighbouring blocks. It is found that the dislocations are distributed very unevenly in the crystal and most of them form complicated boundaries of blocks, similarly as with ionic crystals. The distribution of dislocations is also discussed from the point of view of their formation and conclusions are reached as to the preparation of single crystals having a smaller number of dislocations.

---

Fe-Si,

- Fe-4,2%Si, , . . , , — . , , . .

---

---

The author is indebted to Candidates of Mathematics and Physics, F. Kroupa and J. Kaczér, for careful reading and advice whereby they helped to give greater depth and accuracy to this paper. He thanks Z. Tahal and M. Honegrová for initiative shown in helping to prepare the single crystals and during exacting experimental work, and S. Kadeková for aid in adjusting the spectrometer.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

Das Anhaften von Exzitonen an Störstellen des Kristallgitters

Zusammenfassung Es wird der Proze des Anhaftens von Exzitonen an Vakanzen und F-Zentren in den Ionenkristallen studiert. Die Bewegung der Exzitonen im Felde der Vakanz und des F-Zentrums wird in adiabatischer Annäherung untersucht. Mit Hilfe der klassischen Methoden werden die Wirkungsquerschnitte des Anhaftens des Exzitons an den Vakanzen und F-Zentren bestimmt und diskutiert.

---

F- . F- . F- .

     

Thermoemission und Photoemission von Natriumchlorid

Ohne Zusammenfassung

---

Nacl

     

P-polarized nonlinear surface polaritons near the surface of a saturable self-defocusing medium: Threshold case

We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: =_xx=_zz=₀+a|E|²/(1+b|E|²), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter ₀ is positive, b is non-negative, and a and ₁ are negative (₁ is the dielectric function of the linear medium); ₀>|₁|.     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

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.

---

. . . .

     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

---

, , (. . , ). (18), -(24), -(27) (31). , ; .

     

2- And 3-cochains in 4-dimensional SU(2) gauge theory

Explicit formulae are derived for the 2- and 3-cochains _uvq ⁽²⁾ (i, j, k) and _uvq ⁽²⁾ (i, j, k, ) in SU(2) gauge theory in 4 dimensions. It turns out that _uvq ⁽²⁾ (i, j, k, ) is given by the volume of a spherical tetrahedron spanned by the gauge transformations relating the gaugesi, j, k, l.     

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.     

К ТЕОРИИ РЕЗОНАНСНОЙ МИГРАЦИИ ЭНЕРГИИ ВОЗ БУЖДЕНИЯ В ТВЕРДЫХ ТЕЛАХ

- - . - .     

Мезонные распады лег ких гиперфрагментов

, . . , °. K^–- , .

---

The meson decay of light hyperfragments

The binding energies of five types of light hyperfragments, i. e. of atomic nuclei of light elements containing one hyperon instead of one neutron, were measured. The hyperfragments originated by means of the interaction of K^– mesons with the nuclei of light elements, contained in the emulsion.

     

ИЗМЕНЕНИЯ ТОНКОЙ СТР УКТУРЫ МОЛОТОГО КОБА ЛТА

- , . , , - . - , , , - .     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

The λN interaction and structures of the16–18O hypernuclei

The shell model without the nuclear centre-of-mass spuriosity is applied to ^16,17,18O isotopes, predicting the bunched and dense hypernuclear energy levels. The (K^–, ^–) reaction cross sections are calculated at several angles with the =0° ones being in good agreement with the experimental data on ¹⁶O and ¹⁸O. The realistic N effective interaction derived on the basis of the Nijmegen Model-D is employed and the N J=0⁺ pairing correlation is found to be repulsive, which is reflected in the¹⁸O(K^–,^–) ¹⁸O excitation function.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The author is thankful to Professor H. Bando. Professor Y. Yamamoto and Professor H. Ikeda for collaboration and useful discussion.