The classical theory of nuclear spin interaction in a ferromagnet

The Hamiltonian of nuclear spin interaction in a ferromagnet is derived by the classical method, which introduces the precession of nuclear spin into the equation of motion for magnetization. From this it is shown that the interaction Hamiltonian also depends on the magnitude and sign of nuclear precession frequency _N and the damping constant of ferromagnetic resonance A. The calculation of these parameters makes the Suhl [1] quantum mechanical derivation of the Hamiltonian of nuclear spin interaction in a ferromagnet more accurate. The influence of these parameters on the relaxation timeT ₂ is also discussed and is applied to the case of cubic cobalt.

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. , _N . , [1] - . ₂ .

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In conclusion the author thanks Dr. L. Valenta for significant remarks and valuable advice on this work. He also thanks J. Kvasnica and Z. roubek for suggestive discussions.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Magnetization coils without iron core for high field intensities

A new theory of rectangular coils without an iron core is described which amends the old one of Fabry and Bitter. It enables us to compute field intensities in coils having very small openings, which the old theory could not do.

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, , , .

     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

Quantum-resolved fluorescence excitation spectra of SnO free radical

TheA ¹ –X ^{1 +} system of SnO is studied by laser- induced fluorescence excitation spectroscopy using isotopically enriched tin Sn¹¹⁶. The rotational structure analysis has been carried out for 6-0, 5-0, 2-0 bands. All these spectra were well resolved only with few perturbed lines in 2-0 band. Rotational constantsB ₂,B ₅,B ₆ and henceB _e , _{e e} have been obtained for the Sn¹¹⁶O molecule. An extension of perturbation study on 4-0 band has been made showing the maximum perturbation occurs at different J values for different isotopes.     

TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

Power law growth for the resistance in the Fibonacci model

Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n) (n),n,l ²(),, wherev(n)=[(n+1)]–[n],[x] denoting the integer part ofx and the golden mean , give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal.     

C λ-extended oscillator algebra and parasupersymmetric quantum mechanics

The C -extended oscillator algebra is generated by {1, a, a , N, T}, where T is the generator of the cyclic group C of order . It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be easily exhibited using the representation theory of GDOAs and their carrier spaces show a Z-grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p = – 1.     

Some applications of the discrete fourier transform to problems of crystal lattice deformation I

The theory of the discrete Fourier transform [1], [2] is applied in solving a system of difference equations describing the positions of atoms in a deformed crystal lattice. The crystal lattice is approximated by the Born-Kármán model modified to include the internal energy of the undeformed crystal.

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, , , [1] [2]. - , , .

     

Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

The effect of the orientation of zinc single crystals and of the rate of growth on the direction of cell substructure

The effect of the orientation of zinc single crystals and the rate of growth on the direction of the formation of cellular substructure is observed. A model accounting for the observed dependences is proposed.

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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.     

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.     

Relative coarse-graining

The problem of statistical inference based on a partial measurement (coarse-graining) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (relative coarse-graining). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal equilibrium with an unknown reservoir, and the position measurement of a one-dimensional particle. It is shown that some of the limitations of the usual theory are a consequence of the fact that it is restricted to equidistributed (symmetric) a priori states.     

Homogenität,Kovarianz und Relativität

Zusammenfassung Es werden zwei Begriffe: Homogenität des Raumzeitkontinuums und Kovarianz der Gleichungen, wie sie in der Relativitätstheorie gebraucht werden, definiert und erläutert. Es wird gezeigt, doss die beiden Begriffe wesentlich verschieden sind und in Form nichtäquivalenter mathematischer Bedingungen ihren Ausdruck finden. Trotzdem werden beide Begriffe sowohl von Einstein, als auch in der Literatur über Relativitätstheorie mit einem und demselben Wort Relativität bezeichnet. Der Missgebrauch des Wortes Relativität bedeutet nicht nur einen terminologischen Fehler, sondern spricht auch von einem ungenügenden Verständnis der Grundidee der Relativitätstheorie, besonders der sog. allgemeinen Relativitätstheorie. Versteht man unter Relativität Homogenität des Raumes, so ist in der sog. allgemeinen Relativitätstheorie überhaupt keine Relativität vorhanden. Versteht man dagegen unter Relativität Kovarianz der Gleichungen, so steckt in jener Theorie nicht mehr Relativität, wie z. B. in den unrelativistischen Bewegungsgleichungen, welche ebensogut eine allgemein-kovariante Formulierung gestatten (Lagrangesche Gleichungen 2-ter Art). Die Bezeichnung allgemeine Relativitätstheorie ist daher irrefuhrend. Die geniale Theorie Einsteins ist eine reine Gravitationstheorie. , No 4, . 131, 1955. (RhilosophischeFragen No 4, S. 131, Moskau 1955. Ins Deutsche über setzt vom Verfasser).     

Multifractality and scaling in disordered mesoscopic systems

We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, thef() spectrum. The analysis off() spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then thef() spectra of normalized scaling variables must be universal. The critical exponentv of the correlation length is determined by the value (0) wheref() takes its maximum and the scaling exponent of normalizationxv ^–1=(0)+x. As an illustrative example we calculate numerically thef() spectra of eigenstates in the critical regime of 2d disordered electron systems in high magnetic fields. We find similarf() spectra indicating universal log-normal distributions of scaling variables.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Differential calculus on quantum spheres

Three-dimensional differential calculus on quantum spheres S _infc ^sup2 ,]–1, 1[{0}, c[0, ], is introduced and investigated. Spectra of generalized Laplacians are found. These operators are expressed by generalized directional derivatives. Classical limits of these objects are obtained and a simple approach to quantum mechanics on a quantum sphere is presented.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

К В. Ч. НАГРЕВУ РАЗРЕЖЕННОЙ ПЛАЗМЫ

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