On the relation between weak and strong invariance of differential equations

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a strongly invariant equation exists, then all weakly invariant equations differ from it only by an arbitrary multiplicative factor. If no strongly invariant equation exists, then cohomology theory can be used to simplify the search for weakly invariant equations.     

The influence of a small electric perturbation on the electroluminescence curve of ZnS-Cu

The influence of a small electric perturbation of variable phase on the brightness wave of alternating electroluminescence of ZnS-Cu is investigated. The results are compared with the model described in [1]. The increase in the number of ionized activators after switching on the electric field is studied and is found to reach equilibrium. after about 50 to 150 sec.

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ZnS-Cu

ZnS-Cu. , [1]. , 50–150 s.

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In conclusion the author thanks M. Mokonová for cooperation in evaluating the results of measurement.     

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.

     

Crossing relations derived from (Extended) Relativity

Recently, Special Relativity has been straightforwardly extended to Superluminal inertial frames and faster-than-light objects. The Extended Relativity theory not only allowed building up a self-consistent classical theory of tachyons, but reveals itself useful also for the understanding of standard (subluminal) physics, i.e. of usual particles. In this paper, it is shown that Extended Relativity allows: (i) deriving the usual Crossing Relations of elementary particle (high-energy) physics; and (ii) deriving the CPT-covariance theorem as a particular case of G-covariance (i.e., covariance under the new group of Generalised Lorentz transformations, both subluminal and Superluminal).In this framework, the Analyticity postulate is unnecessary: it is better substituted by the G-covariance requirement.Moreover, new crossing-type relations are predicted on the basis of mere Extended Relativity. They may well serve as a test for relativistic covariance of force fields like strong interactions and, particularly, weak interactions, and possible new interaction fields (whicha priori are not relativistically covariant).     

Imaging pattern formation: Bridging the pressure gap

Two surface-sensitive optical imaging methods, Ellipso-Microscopy for surface Imaging (EMSI) and Reflection Anisotropy Microscopy (RAM) are introduced. They allow imaging of pattern formation on surfaces, e.g., due to submonolayer coverages of adsorbates, at any arbitrary pressure.In spatio-temporal pattern formation during heterogeneously catalysed reactions this bridges the pressure gap between well-defined UHV experiments and real catalysis. For the CO oxidation on Pt(110), the parameter space for pattern formation was extended up to 100 mbar, i.e., by 5 orders of magnitude compared to earlier investigations by Photo-Emission Electron Microscopy (PEEM) which had to be conducted below 10^–3 mbar. With increasing pressure, the synchronisation mechanisms responsible for the observed pattern showed a gradual shift from reaction-diffusion to thermal-kinetic coupling unveiling previously unseen features of pattern formation in catalysis.     

Surface topology investigation for ancient coinage assessment using optical interferometry

In order to demonstrate the capabilities of white-light interferometry depth profiling (WLI-DP) for ancient coinage assessment, we investigated a series of notorious 1786 gold coins, bearing Louis XVIs horned effigy, and allegedly minted in Strasbourg. Scanning electron microscopy as well as WLI-DP observations unambiguously indicate that both previously differentiated single- and double-horned varieties originated from a unique minting tool. Moreover, from topological measurements, we infer that single-horned coins, rather than wearing out into double-horned coins, proceeded from the latter variety during minting by progressive failure of an already altered die. Whereas present observations do not exclude initial forgery, they suggest that protrusions resulted from progressive incidental in-service die deterioration. PACS 81.70.Fy; 07.60.Ly; 61.16.Bg; 81.40.Pq     

Maximal structures of determinate propositions in quantum mechanics

I formulate and answer some questions concerning maximal structures of determinate quantum propositions, i.e., maximal structures of propositions that can be taken as having definite (but perhaps unknown) truth values for a given quantum state. The basic constraint on such structures is the Kochen and Specker no-go hidden-variables theorem, which demonstrates that no value assignment to certain finite sets of observables can preserve the functional relations between commuting observables. The problem I want to consider is how large we can take the set of determinate observables without violating the functional relationship constraint. I show how to construct maximal determinate sublattices of quantum propositions that are unique, subject to certain constraints, and I comment on the relevance of this go theorem for the interpretation of quantum mechanics.     

Faux-boolean algebras,classical probability,and determinism

It is possible to define, for any quantum system, an algebra of definite-valued events—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain pseudo-Boolean algebra.     

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.     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an electron, interacting with massless, relativistic bosons, photons, is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of photons by the electron; but electron-positron pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed electron is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one–electron states with propagation estimates for the electron and the photons.Dedicated to Freeman Dyson on the occasion of his 80th birthdayWork partially supported by U.S. National Science Foundation grant DMS 01-00160.Acknowledgement. We thank V. Bach for his hospitality at the University of Mainz, where part of this work was done, and we are indebted to Gian Michele Graf for pointing out a serious gap in an earlier version of this paper. We also thank one of the referees for pointing out many typos and some small errors.     

Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

A quantum-group-like structure on noncommutative 2-tori

We show that on noncommutative 2-tori, there are natural structures which have analogous formal properties as Hopf algebra structures, but where the comultiplication has values in a deformation of the tensor product.Supported by Project P 7724 PHY of Fonds zur Förderung der wissenschaftlichen Forschung.     

Ghost lines in Mössbauer relaxation spectra

The appearance in Mössbauer relaxation spectra of ghost lines, which are narrow lines that do not correspond to transitions between real hyperfine energy levels of the resonant system, is examined. It is shown that in many cases of interest, the appearance of these ghost lines can be interpreted in terms of the relaxational averaging of one or more of the static interactions of the ion.     

Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.     

Mass splitting in relativistic quantum field theory

Null plane integrals of certain classes of tensor densities, conserved or non-conserved, may define symmetric operators on dense subspaces of the in and out states. These operators annihilate the vacuum and may satisfy a Lie algebra. In particular, the possibility that a finite number of null plane charges, which includes the Poincaré generators, close on an algebra whose irreducible representations contain particles with different masses is considered. The situation in which the Lie algebra is defined on a dense domain which is not from the in and out states is discussed. Some algebraic hypotheses other than that of a Lie algebra in the usual sense are briefly considered; in these cases there can be no mass splitting.Supported in part by the U.S.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel.     

Reversible and endoreversible computing

Reversible combinatorial computers are built from basic cells with a three-bit digital input and a three-bit digital output. Such a computer can calculate both from left to right and from right to left, such that input pins and output pins are indistinguishable. In order to perform a calculation in a specific direction, an electric field should be applied externally. The inevitably frictional losses occur in the lines supplying the computer with the input data and in the lines draining the calculation results to the output registers. Such behavior is analogous to the endoreversible operation of heat engines and other energy converters.     

Perturbed periodic Hamiltonians: Essential Spectrum and exponential decay of eigenfunctions

Spectral properties of – +V(x), whereV(x) lies in a neighbourhood of the periodic case and describes various models of disorder, are studied. We prove the exponential decay of generalized eigenfunctions corresponding to energies in the resolvent set of the unperturbed periodic Hamiltonian, as well as the stability of the essential spectrum for the dislocation disorder in two dimensions.     

On the photo-electroluminescence of ZnS-Cu

The influence of weak ultra-violet irradiation on the brightness waves of electroluminescence is investigated for two types of ZnS-Cuphosphors. The observed effects (increase in brightness in the primary peak and its phase shift, the disappearance of the secondary peak) are explained on the basis of present-day conceptions on electroluminescence.

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ZnS-Cu

ZnS-Cu. ( , ) .

     

Theory of ferromagnetic resonance line shape in insulators

The paper discusses the absorption of the energy of a high-frequency field by a magnetic sample from the point of view of the interaction of spin waves with photons and spin waves amongst themselves. A general expression for the form of the absorption curve is derived, using the method known from the quantum theory of radiation and assuming very weak fields.

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The author thanks S. Krupika, Candidate of Sciences, for the exceptional interest taken in this work, for advice and a number of helpful and critical remarks.