Equidistant spectra of anharmonic oscillators

Some representative potentials of the anharmonic-oscillator type are constructed. Some corresponding spectra-shift operators are also constructed. These operators are a natural generalization of Fok creation and annihilation operators. The Schrodinger problem for these potentials leads to an equidistant energy spectrum for all excited states, which are separated from the ground state by an energy gap. The general properties of the dynamic system generated by spectral-shift operators of third degree are analyzed. Several examples of such anharmonic oscillators are discussed. The relationship between the eigenvectors of the Schrodinger problem and a certain type of nonclassical orthogonal polynomials is established.     

Algebraic independence of values of a certain class of hypergeometric functions

We prove a general theorem on the algebraic independence of values of hypergeometric E-functions and their successive derivatives at algebraic points for the degenerate case in which substantial cancellations occur in numerators and denominators of coefficients of the series in powers ofz of the functions considered.Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 402–414, March, 1996.     

Transformation of the TE polariton spectrum of the one-dimensional magnetic photonic crystal under conditions of the quadratic electro-optic effect

A one-dimensional magnetic superlattice of the easy-axis antiferromagnet-nonmagnetic insulator type is considered in an external static electric field applied perpendicular to the easy magnetization axis. The conditions are determined under which the quadratic magneto-optical interaction leads to a number of specific features in the conditions of localization and propagation of collective magnetic s polaritons.     

Polariton dynamics of a one-dimensional gyrotropic magnetic photonic crystal in a dc electric field: II. Surface waves

Localization and dispersion of collective magnetic TE and TM polaritons are analyzed for a semi-infinite, one-dimensional, magnetic photonic crystal of the compensated antiferromagnetic-nonmagnetic dielectric type in the presence of orthogonal magnetic and electric fields. The case where easy magnetization axis is orthogonal to the external electric field is considered.     

Powerful Cherenkov oscillators with 2D distributed feedback

The feasibility of using 2D distributed feedback based on 2D planar and coaxial Bragg structures for generating spatially coherent radiation from rectilinear ribbon and tubular electron beams is studied. One-section and sectional Cherenkov masers are analyzed. In the former design, a 2D Bragg structure acts as a resonator and a periodic slow-wave system simultaneously. In the latter (sectional) design, radiation is synchronized in a 2D Bragg structure that is placed at the cathode end of the interaction space and couples longitudinal and transverse (azimuthal) wave flows. The wave is amplified by the electron beam mainly in the fairly long middle section. The output (collector) part contains a standard 1D Bragg structure that partially reflects the amplified radiation toward the cathode and closes the feedback circuit. It is shown that dissipation introduced into the 2D Bragg structure of the sectional design makes it possible to increase one of the transverse sizes of the system to ∼10³ wavelengths with the energy exchange efficiency and one-frequency masing mode stability remaining the same. With such an overdimension, the millimeter-wave radiation integral power may reach a gigawatt level.     

Measurement of Cross Sections for Inclusive Forward Charged Hadron Production in Carbon–Carbon Collisions at Beam Energy of 19.6 GeV per Nucleon

Physics of Atomic Nuclei - The invariant cross sections for forward charged-hadron production at zero angle in carbon–carbon collisions at a beam kinetic energy of 19.6 GeV per nucleon were...     

A new method of synthesis of substituted 1-(1H-imidazole-4-yl)-1H-1,2,3-triazoles and their fungicidal activity

Based on the deoxygenation reaction of 1-(1-tert-butyl-3-nitroazetidine-3-yl)-1H-1,2,3-triazoles a new method for the synthesis of substituted 1-(1H-imidazole-4-yl)-1H-1,2,3-triazoles has been developed. Fungicidal activity of these compounds has been investigated at a range of phytopathogenic fungi.     

Quantum nondemolition measurements in systems with nonstationary squeezing of quantum noise

Summary A Weber detector with optical readout system is considered. The measuring device consists of circulators, homodyne detector and two degenerate parametric amplifiers (or four wave mixers), modifying vacuum fluctuations of the load. In this scheme the greater the squeezing of backaction noise, the smaller the measurable force acting on the mechanical resonator. Postulation of gedanken state reduction is not necessary in our model.

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Riassunto Si considera il rivelatore Weber con sistema di lettura ottico. Lo strumento di misura consiste di circolatori, di un rivelatore omodino e due amplificatori parametrici degenerati (o quattro miscelatori d'onda), che modificano le fluttuazioni nel vuoto del carico. In questo schema, maggiore è la compressione del rumore di retroazione e minore risulta la forza misurabile che agisce sul risonatore meccanico. Nel modello in questione non è necessario postulare la riduzione dello stato concettuale.

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Резюме Рассматривается детектор Вебера с оптической системой считывания. Измерительная аппаратура состоит из циркуляционных насосов, детектора и двух вырожденных параметрических усилителей (или преобразователей четырех волн), преобразуюших вакуумные флуктуации нагрузки. В этой схеме, чем меньше измеряемая сила, действующая на механический резонатор, тем больше подавление шума. В нашей модели не требуется постулирование преобразования состояния.