Separation of variables in the wave equation. Sets of the type (1.1) and the algebra SU(1.2)

It is shown that for the wave equation in Minkowski space all complete sets of symmetry operators that contain one istropic operator reduce to sets in which the isotropic operator has the form /x⁰+/x³.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 102–105, February, 1991.     

Extrapolation of NEMO Technique to Future Generation of 2β-Decay Experiments

Possibilities of NEMO technique for future neutrinoless double-beta-decay experiments are discussed. Main idea is to have a realistic project with planned sensitivity for half-life on the level (1-2) × 10²⁶ y (sensitivity to neutrino mass (0.05-0.1) eV). It is demonstrated that this can be achieved using improved NEMO technique to investigate 100 kg of ⁸²Se. Possible improvements of NEMO technique and background conditions are discussed. Scheme of future SUPERNEMO detector and main characteristics of experiment are presented. Such detector can be used also to investigate 0 decay in ¹⁰⁰Mo, ¹³⁰Te and ¹¹⁶Cd with sensitivity up to (5-10)×10²⁵ y (or with sensitivity to neutrino mass 0.1 eV).     

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.     

Some tree-like Julia sets and Padé approximants

The Julia set B for T(z)=(z–)², the equilibrium electrostatic measure on B, the associated orthogonal polynomials, P _n, and the Padé approximants to the moment-generating function for are considered. When 02, the locations of the zeros and poles for the Padé approximant sequence (z), n=0, 1, 2, ..., are described precisely as vertices of trees of analytic arcs associated with B. For infinitely-many values of B is the closure of these trees. P ₂ ⁿ is shown to be a Chebychev polynomial on B for positive, attaining its maximum modulus at 2 ⁿ⁺¹ points of B if 2.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-80002731     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

— —10 ^–4 —10 ^–2 . , . , , , , , .     

Зависимостъ послесв ечения люминесценци и от толщины образца

, , . .     

К изучению пространс тв между электродами в кратковременных эл ектрических разряда х с болъшой силой тока

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A contribution to the study of electrode spaces of high-current short-duration electric discharges

The electrode spaces of high-current short-duration discharges are analyzed using the method of artificial contraction (limiting of the active surface of the electrodes). It was shown that evaporation of the electrodes during the discharge can be regarded as one of the main factors causing thermal contraction of the channel on the surface of electrodes, high-current density on the electrodes and enabling the independent existence of partial spots.

     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Precision test of the isotropy of light propagation

We report on a test of the isotropy of light propagation performed by comparing the resonance frequencies of two orthogonal cryogenic optical resonators subject to Earths rotation over 1yr. The technical aspects of the experiment are discussed and the analysis of the data is presented in detail. For a possible anisotropy of the speed of light c, we obtain c/c₀=(2.6±1.7)×10^-15. Within the general extension of the standard model of particle physics, we extract limits on seven parameters at accuracies down to 10^-15, improving the best previous result by about two orders of magnitude. Within the Robertson–Mansouri–Sexl test theory, this implies an isotropy-violation parameter --1/2=(2.2±1.5)×10^-9, about three times lower than the best previous result. PACS 03.30.+p; 12.60.-i; 06.30.Ft     

Semiconducting structures and devices based on gallium arsenide with deep centers

We have examined the characteristics of nontraditional gallium arsenide -v-n type device structures, in which p-n junctions are formed by doping the semiconductor with deep centers. The properties of -v-n structures are established by processes of charge trapping at deep centers under the effect of an external bias or exposure to a wide spectral range of electromagnetic radiation. The nature of formation of S-type negative differential resistance for a reverse biased -v-n structure and the mechanism of high speed switching (with a switching time of (0.4–5)×10^–10 sec) were analyzed. The results of an investigation of the effects of optical radiation, x-rays, -radiation and high energy charged particles on the structures are discussed and the characteristics of new devices constructed using -v-n structures are presented. These devices include high speed avalanche S-diodes and triodes, wide spectral band photodiodes (=0.2–10 µm) and detectors for x-rays, -radiation, and relativistic electrons.V. D. Kuznetsov Siberian Physical-Technical Institute, State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 33–44, September, 1992.     

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.

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Anomalous temperature dependence of the magnetic field penetration depth in superconducting UBe13

We report the first measurements of the magnetic-field penetration depth in the heavy electron superconductor UBe₁₃, performed using a SQUID magnetometer. We find the temperature dependence of (T)-(0) to follow aT ² law at low temperatures, giving further evidence of extreme gap anisotropy in this compound. We calculate the temperature dependence expected for a variety of anisotropic states, including those representing certain classes of exotic pairing. In general situations, the supercurrent is not parallel to the vector potential, and a more complicated field penetration takes the place of the normal Meissner effect. We argue that the data are consistent with an energy gap with point nodes on the Fermi surface but inconsistent with the large value of the Landau parameterF ₁ ^S expected for a translationally invariant Fermi liquid with large effective mass.     

Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B₂, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B₄⁽⁰⁾=197.3(1)B₂ and one excited state with B₄⁽¹⁾=25.5(1)B₂. We compare our results to recent predictions for N-body bound states with large N1.On leave from FZ Jülich, Institut für Kernphysik (Theorie), D-52425 Jülich and HISKP (Theorie), Universität Bonn, Nußallee 14–16, D-53115 Bonn, Germany     

Канал кратковременн ого силъноточного электрического разр яда

, ( 10² sec, , 10⁴ A), .

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Channel of short-time high-intensity electric discharge

By the spatial expansion of the radial cross-section of the channel of the given type of discharge (duration 10² sec and maximum intensity smaller than 10⁴ A)and by measuring some of its electrical quantities information was obtained on its channel and the influences bringing about the forming process.

     

ОПРЕДЕНИЕ ВНУТРЕННЕГО КВАДРУПОЛЬНОГО МОМЕНТА Ег162 ИЗ фОТОЭЛЕКТРИЧЕСКОГО ИЗМЕРЕНИЯ ИЗОТОПИЧЕСКИХ СМЕЩЕНИЙ ЛИНИЙ Ег I И Ег II

The isotopic shifts in Er I and Er II spectra were investigated by means of a recording spectrometer with a Fabry-Perot interferometer. The experimental technique of measuring the shifts of the spectral lines consists of using monoisotopic sources of light and a photoelectric record of alternating interference patterns corresponding to the different isotopic components. The values of the relative shifts of 30 lines of erbium and the data of the deformation parameters of the nuclei of Er¹⁶⁶ and Er¹⁶⁸ were used for determining the intrinsic quadrupole moment of Er¹⁶². It follows then from the theory of the isotopic effect in the spectra of elements with deformed nuclei, that the value of the intrinsic quadrupole moment isQ ₀(Er ¹⁶²)=(7·25±0·30)× ×10^–24 cm².

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The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Combinations of Observables

This article begins with a review of the framework of fuzzy probability theory.The basic structure is given by the -effect algebra of effects (fuzzy events) E(,A) and the set of probability measures M ⁺ ₁ (, A) on a measurable space (,A). An observable X: B E(, A) is defined, where (, B) is the value spaceof X. It is noted that there exists a one-to-one correspondence between states onE(, A) and elements of M ⁺ (, A) and between observables X: B E(,A) and -morphisms from E(, B) to E(, A). Various combinations ofobservables are discussed. These include compositions, products, direct products,and mixtures. Fuzzy stochastic processes are introduced and an application toquantum dynamics is considered. Quantum effects are characterized from amonga more general class of effects. An alternative definition of a statistical map T:M ⁺ ₁ (, A) M ⁺ ₁ (, B) is given.     

Nonlinear superposition for Liouville's equation in three spatial dimensions

We derive in 3+0 dimensions exact solutions of Liouville's equation ²=exp , by applying the Bäcklund transformation technique in conjunction with the principle of nonlinear superposition. The procedure, which is later extended to 3+1 dimensions, yield, as a byproduct, particular solutions of ² and ² =exp (² +² ).     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.