The quantum Hall effect (QHE) is considered from the standpoint of the general theorems of quantum field theory and is interpreted as a quantum macroscopic phenomenon due to a spontaneous break of symmetry of the corresponding quantum system. An effective field model of QHE is suggested and a relationship between this model and the two-dimensional Higgs abelian model is established. This made it possible to determine what seems to be the true vacuum state in the case of the fractional quantum Hall effect, which turned out to be a nondegenerate $|\theta \rangle$-vacuum state.
Show AbstractVarious methods for separating the ultraviolet and infrared divergences in two-dimensional nonlinear sigma models are discussed. An infrared regularization is proposed that takes into account the ultraviolet renormalization effect in the preceding orders and makes it possible to obtain invariant ultraviolet counterterms by the background field method.
Show AbstractThe possibility of constructing a theory in which the space-time topology is determined by the dynamics of closed boson strings is analyzed. The initial object in the theory is a topological space of the contours which determines the form of the string interaction vertex. A cohomological complex and a topologically invariant action are constructed on the space of contours. The equations of motion obtained by varying the action coincide with the condition of closure of differential cohomology forms. The analysis is carried out in the form of an expansion with respect to the string coupling constant. The zeroth- and firstorder approximations are considered. Restrictions imposed on the space-time topology by the string dynamics are found. In what follows, by the space-time is meant an intermediate finite-dimensional space obtained from the original infinite-dimensional space of the contours and containing singularities. To pass to a smooth physical space-time it is necessary to pass to the massless limit, which will be the subject of another paper.
Show AbstractThe effective action in the gauge theory for the (2+1)-dimensional space-time was considered and its dilatational invariance was proved. Based on the dilatational invariance, we demonstrated the finiteness of the effective action in all orders of perturbation theory.
Show AbstractThe problem of uniqueness of the determination of diffusion coefficient from data on the concentration field is investigated for carbonitriding models. For a more general inverse problem the uniqueness is proved for the normal solution with respect to the polynomial coefficients of the parabolic system of equations.
Show AbstractIn this paper consideration is given to the application of the measurement reduction method to the problem of introducing graphical information into a computer with a digitizer. An algorithm is described, which takes into account the errors arising in the graph pickup and the position of the graph on the digitizer plotting board. The algorithm makes it possible to obtain the most precise values of the coordinates of the graph points. Estimates for the concomitant error are presented.
Show AbstractSelf-similar soliton-like solutions to a system of two nonlinear Schr$\stackrel{..}{o}$dinger-type equations (NSE) for various sets of coefficients have been studied theoretically and numerically. In the case of equality of the corresponding coefficients in the two equations of the system, a family of solitons of a new class with complex amplitude modulation has been found. The existence and uniqueness theorem for the NSE system has been proved and the related finite-difference scheme investigated.
Show AbstractBased on the analytical properties of the pion formfactor and the sum rules of quantum chromodynamics (QCD), the values of the gluon and the four-quark condensates are determined. The nonperturbative structure of the pion form-factor leads to an increase in the condensate values as compared to the standard ones.
Show AbstractThe use of the reduction method without a priori information, invariant relative to nuclear models, helps improve the energy resolution of experimental data up to a value equal to one or two energy steps at which these data are measured. This energy resolution, which can be several times higher than the experimentally attainable one, corresponds to the full width at half maximum of a new apparatus function synthesized in the process of solving the problem and having a shape close to Gaussian.
Show AbstractThe effect of external fields on the luminescence of the (0.1-1) $mg$ $ml^{-1}$ aqueous glycyltryptophan solution was studied. It was found that the solution "memorizes" the prolonged external action of both a constant magnetic field with induction of 0.1 T and a linearly polarized quasimonochromatic light-wave field with intensity of about 1 $W m^{-2}$. On termination of the exposure, the relaxation processes had a nonmonotonic behavior of a cyclic character with characteristic times of the order of a few tens of minutes. The results obtained were interpreted in terms of the concept of an interrelation between structural rearrangements in water and conformational variations of solute molecules.
Show AbstractThe method and equipment are described which allow remote measurements of the horizontal distributions of the phytoplankton photosynthetic activity to be carried out in situ aboard a moving vehicle (ship, plane, or helicopter). In the course of measurements the relative yield of the variable fluorescence of chlorophyll $a$ is determined, this quantity characterizing the efficiency of light utilization in the primary reactions of photosynthesis. It is shown that for the measurements to be correct, the photon fiux density of the activating pulse in the volume probed must be no smaller than $5 \times 10^{22} cm^{-2} s^{-1}$, that of the probing pulse must not exceed $10^{22} cm^{-2} s^{-1}$, and a time interval of 40-70 μs between these pulses must be ensured. The results of laser determinations of the photosynthetic activity of phytoplankton over extensive water areas of the North-West Atlantic are discussed.
Show AbstractThe specific features of the fluorescent response of dissolved organic substance (DOS) in water to optical excitation are examined: reversible and irreversible changes in the fluorescence spectra and in the fluorescence excitation and absorption spectra, induced by ultraviolet radiation and temperature variations. The results obtained are used to develop methods for diagnosing DOS, which is one of the most abundant components of natural media.
Show AbstractThe scattered light correlation spectroscopy and luminescent probe techniques have been applied to study aqueous ethanol solutions. It is shown that adding $С_2Н_5ОН$ to water in concentrations below 10 vol.% results in adsorption of ethanol molecules on the surface of clusters, which causes an increase in their volume. Adding more ethanol destroys the clusters. An analysis of the polarization and kinetic characteristics of eosin luminescence shows microstratification to occur in aqueous ethanol solution in the range of ethanol concentrations from 20 to 80%. The scattered light correlation characteristics have been used to detennine the volume of one of the solution microphases.
Show AbstractThe probability of enhanced concentration of microdefects in a small volume, irrespective of its shape, was determined. This and a Griffith's type representation were used to determine the probability of rupture depending on the stress applied and to analyze the size effect and the dependence of ultimate strength on the average concentration of defects.
Show AbstractThe paper is devoted to the statement and computer solution of the inverse problem on the determination of the parameter controlling the regime of specimen cooling during hardening by providing the required cooling rate at a given depth. The investigation results can serve as a basis for elaborating automatic control systems for the technological process of thermal treatment of machine elements.
Show AbstractIn the ferromagnetic $HgCr_2Se_4$ semiconductor ($Т_с\approx108$ K), apart from the characteristic redshift of the edge of optical absorption, a redshift of photoconductivity and photo-emf spectra was also observed with decreasing temperature. The influence of magnetic ordering on the band structure also showed itself in the temperature and magnetic field dependences of these effects. Besides the peak near $Т_с$, the dependences of the relative variation of photoelectric effects in the magnetic field on temperature exhibited an additional peak at $Т>Т_c$ for the light with an energy $h\nu$, which is close to the forbidden band width. This peak may be expected to appear in the paramagnetic region for other magnetic semiconductors, too.
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