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.     

Theory of moving striations in plasma of D-C discharge I. Basic equation and its general solution

As a base for the theory of moving striations a partial integro-differential equation (26) is derived from the equations of continuity (1), (2), the Laplace-Poisson equation (3) and relation (4) between the electric field and the temperature of the electrons. Apart from the processes necessary for the actual formation of striations according to [1] and for the amplification of the wave of stratification according to [2], the equation also includes the processes defining the Debye length of the electrons, the influence of the axial electric field and of its local deflections on the motion of current carriers and the direct influence of the deviations in concentration of the electrons on the rate of production of current carriers. In deriving the equation the main attention is paid to the physical sense of the mathematical operations applied. The general solution is found by the method of the two-sided Laplace transformation and is described by triple integral convolution (42).

---

I.

(1), (2), - (3) (4) (26). , , [1], , [2], , , . . (42).

     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Спектралъный метод о пределения изотонно го состава свинца. Частъ I

, . , . - . PbI4058 Å . , . 1000000. , , . - , .     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

Twisted Lie Group C*-Algebras as Strict Quantization

A nonzero 2-cocycle Z2(g, R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie–Poisson structure on the dual Lie algebra g*, leading to a Poisson algebra C (g*()). Similarly, a multiplier c Z2(G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C-algebra C*(G,c). Further to some superficial yet enlightening analogies between C (g*()) and C*(G,c), it is shown that the latter is a strict quantization of the former, where Plancks constant assumes values in (Z\{0})-1. This means that there exists a continuous field of C*-algebras, indexed by 0 (Z\{0})-1, for which A0= C0(g*) and A=C*(G,c) for 0, along with a cross-section of the field satisfying Diracs condition asymptotically relating the commutator in A to the Poisson bracket on C(g*()). Note that the quantization of does not occur for =0.     

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.     

Diffusion parameters of thermal neutrons in diphenyl

The diffusion length, diffusion coefficient and mean life time of thermal neutrons in rigid, Czechoslovak made, diphenyl were measured by the impulse method at the temperature 20°C. The experimental results are discussed.

---

, ( ) 20°C. .

---

---

We thank J. Jadavan and the accelerator group for their co-operation.     

ПРОВОДИМОСТЬ СРЕДНЕ Й ЧАСТИ КАНАЛА КОНДЕНСИРОВАННЫХ РА ЗРНДОВ

. , . . - , 500 10 000 30 500 . - , .     

On the determination of the position of the energy level of surface recombination centres

A detailed analysis of the dependence of the surface recombination velocitys on the surface potential _s leads to the conclusion that the position of the surface recombination level with respect to the centre of the energy gapE _t -E _i does not coincide with the valueq _s *, while the surface recombination velocitys decreases to half its maximum value. The difference between the two quantities is negligible only when the width of the curves( _s ) between the points corresponding to the valuess=1/2s _max is greater than 8kT.

---

s _s , E _t -E _{i s} , s . , s( _s ) , s=1/2s _max, 8kT.

     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПОЛЕМ I

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

---

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.

     

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.     

Усовершенствование рентгенометрическо го метода определения дефекто в решетки третьего ро да в поликристаллическ их и порошкообразных материалах

, . .     

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.     

KL,S → l+l− decays in the quark model of superconductivity type

The probabilities of K_L,S l⁺l^– decays are calculated by considering only the dominant two-lepton channel K_L,S ^{* *} l⁺l^–. The transitions K⁰ X, where X=⁰,, or (700) dominating in the K_L,S ^{* *}decay amplitudes, are described by the effective weak Lagrangian. The matrix elements of four-quark operators are calculated within the framework of the quark model of superconductivity type. It is shown that the leading contribution to matrix elements of K⁰ X transitions comes from the penguin operator matrix elements.     

Electron velocity and momentum density

A null 4-vector ^°, based on Dirac's relativistic electron equation, is shown explicitly for a plane wave and various Coulomb states. This 4-vector constitutes a mechanical model for the electron in those states, and expresses the important spinor quantities represented conventionally byn, f, g, m, j, ,1, ands. The model for a plane wave agrees precisely with the relation between velocity and phase gradient customarily used in quantum theory, but the models for Coulomb states contradict that relation.     

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     

On the validity of an einstein relation in models of interface dynamics

We consider models of interface dynamics derived from Ising systems with Kac interactions and we prove the validity of the Einstein relation=, where is the proportionality coefficient in the motion by curvature, is the interface mobility, and is the surface tension.     

Der Einfluss von Fremdstoffgehalt auf einige Kenngrössen der Verfestigungskurven von Zinkeinkristallen

Zusammenfassung Es wurde der Einfluß von Fremdstoffgehalt: auf die kritische Schubspannung ₀, den Verfestigungskoeffizient _A im BereichA der Verfestigungskurve; die Längea _A des BereichsA, und die Schubspannung _A am Ende des BereichsA, von Zinkeinkristallen untersucht. Es konnte gezeigt werden, daß der Einfluß von Fremdstoffgehalt auf den Wert der kritischen Schubspannung vorwiegend indirekter Natur ist. Die Abnahme des Verfestigungskoeffizienten mit zunehmendem Fremdstoffgehalt kann an Hand erhöhter Leerstellenkonzentration erklärt werden. Das Auftreten des BereichsB wird im Zusammenhang mit der Entstehung von Frankschen Halbversetzungen erwogen.

---

₀, _A , _A . , . . .

---

---

Herrn P. Sirotek bin ich für den Umbau und die Instandsetzung des Polanyiaparates zu Dank verpflichtet. Mein Dank gehört ferner Herrn J. Voráek, für die präzise Durchführung der polarographischen Analysen, Frau I. Ejemová und M. Postránecká, für die Verrichtung der Orientierungsbestimmungen und Rechenarbeiten. Gleichzeitig möchte ich Frl. Svobodová meinen herzlichen Dank aussprechen — sie hat, auf Anregung des Lehrstuhls für mathematische Statistik an der mathematisch-physikalischen Fakultät der Karlsuniversität in Prag, mit großem Verständnis die statistische Auswertung der Meßergebnisse durchgeführt. Herrn Dr. F. Kroupa und Ing. B. esták bin ich für das Durchlesen des Manuskripts sowie wertvolle Hinweise zu Dank verpflichtet. Mein besonderer Dank für zahlreiche fruchtbare Diskussionen und Anregungen gilt Herrn P. Kratochvíl. Herrn Prof. Dr. A. Seeger danke ich ganz besonders für Kritik des Manuskripts und wertvolle Ratschläge.