Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Possibility-theoretic method of measurement reduction

### Yu.P. Pyt'ev

Moscow University Physics Bulletin 1999. 54. N 1. P. 1

A possibility-theoretic model has been applied to solve the problem of reducing a measurement to an ideal instrument.

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## Analysis of light scattering by a particle inside a layer by the method of discrete sources

### E.Yu. Eremina, A.G. Sveshnikov

Moscow University Physics Bulletin 1999. 54. N 1. P. 8

A mathematical model of the problem of light scattering by a particle residing inside a layer on a substrate is analyzed on the basis of the method of discrete sources. A computational algorithm has been constructed. Computation results have been presented for light scattering by particles of various materials.

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## On conditionally well-posed inverse problems

Moscow University Physics Bulletin 1999. 54. N 1. P. 17

The possibilities of a natural conditional well-posed statement and algorithmization of two problems of immunology and seismology are discussed. The results of a mathematical experiment on estimating the modulus of continuity have been presented.

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## Renormalization along the lines: normal and anomalous Ward identities in the Yang-Mills model

### D.A. Slavnov

Moscow University Physics Bulletin 1999. 54. N 1. P. 22

A generating equation for normal and anomalous Ward identities in the Yang-Mills model has been obtained in the framework of the dimensional renormalization along the lines. It has been confirmed that only one-loop diagrams are responsible for the chiral anomalies.

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## Surprises of quantum measurements

### Yu.I. Vorontsov

Moscow University Physics Bulletin 1999. 54. N 1. P. 27

Formal analysis of the state of an object after measuring its coordinate shows that the conditional variance of the momentum may depend on the result of coordinate measurement and be smaller than the momentum variance in the initial state even if there is no correlation between the momentum and the momentum squared with the coordinate. This fact cannot be interpreted on the basis of ordinary statistics, exemplifying still another nonclassical consequence of the quantum theory.

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## Dirac fermion in strong coulomb field in 2+1 dimensions

### V.R. Khalilov

Moscow University Physics Bulletin 1999. 54. N 1. P. 32

The effect of charged fermion pair production hy a strong external Coulomb field in two spatial dimensions is studied. Exact solutions to the Dirac equation have been found for a Coulomb field in 2+1 dimensions. It is shown that the behavior of the lower energy levels of an electron in a strong Coulomb field differs significantly in the cases of two and three spatial dimensions. An equation has been obtained for the critical charge and solved numerically for a simple model. The critical charge in 2+1 dimensions is much smaller than its value for the same model in 3+1 dimensions.

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## Global synchronization in a chain of parametrically coupled quadratic mappings

### A.Yu. Loskutov, S.D. Rybalko

Moscow University Physics Bulletin 1999. 54. N 1. P. 37

A chain of parametrically linearly coupled quadratic mappings was analytically shown to have global synchronization, i.e., that the system tends to a trivial equilibrium state.

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Atomic and nuclear physics

## Determination of electromagnetic form factors of nucleon resonances from data on $\gamma p\to \Delta^{++}\pi^-$ and $\gamma p\to p\rho^0$ reaction cross sections

### E.N. Golovach$^1$, V.S. Zamiralov$^1$, B.S. Ishkhanov$^1$, V.I. Mokeev$^1$, G. Rico$^2$, M. Ripani$^2$, D.A. Rodionov$^1$

Moscow University Physics Bulletin 1999. 54. N 1. P. 42

A method for extracting form factors $N^*$ from the experimental data on cross sections of exclusive reactions $\gamma_{r,v} p \rightarrow \Delta^{++} \pi^{-}$ and $\gamma_{r,v} p \rightarrow p \rho^0$ has been developed. It is shown that the method ensures stable calculation of form factors with an inaccuracy of about 10% if the errors in measuring cross sections of said quasi-two-particle reactions do not exceed 3%.

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## Improving the sensitivity of radiometric systems by signal postdetector digital processing

### V.V. Gladun, A.I. Dubina, Yu.A. Pirogov

Moscow University Physics Bulletin 1999. 54. N 1. P. 46

A digital method is described for processing the postdetector signal that makes it possible to maximize the sensitivity of radiometric systems. The method also allows for adapting radiometric systems to operation in microwave imaging devices using phased antenna arrays in scanning the scenes observed in real time.

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Optics and spectroscopy

## Acoustooptic light modulation in an isotropic medium in the case of strong acoustooptic interaction

### V.I. Balakshy, I.A. Nagaeva

Moscow University Physics Bulletin 1999. 54. N 1. P. 50

The results are presented of theoretical studies into the diffraction of light by an amplitude-modulated acoustic wave in conditions of strong acoustooptic interaction. The diffraction efficiency is calculated for a Bragg-type modulator. It is demonstrated that where the modulation frequency is high enough, the symmetry of the acoustooptic coupling is disturbed so that the diffraction efficiency may be as high as 94% even for a focused light beam.

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Geophysics

## Calculation of associated mass tensor in the problem of the Earth's hard core motion

### S.L. Pasynok

Moscow University Physics Bulletin 1999. 54. N 1. P. 57

We have calculated the associated mass tensor for harmonic oscillations of the Earth's hard core. The consideration of this tensor causes free oscillation periods of the Earth's inner core to increase by approximately an hour. For some values of the core density, the periods of oscillation are close to the experimental ones obtained by D. E. Smylie. The splitting of experimental frequencies can well be interpreted as the splitting of the equatorial mode of free oscillations of the inner core in the gravity field of the asymmetric shell, provided that the latter possesses a corresponding quadrupole moment.

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## "Baromagnetism" of planets and stars

### V.I. Grigor'ev

Moscow University Physics Bulletin 1999. 54. N 1. P. 63

Physical mechanism of formation of magnetic fields of planets and stars associated with differential motions of electric charges in their interior acquired due to the baroelectric effect is considered. This polarization-kinetic mechanism, not discussed previously, allows an understanding, in particular, of how tidal effects cause the noncoincidence of the geographic and magnetic axes of celestial bodies.

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Astronomy

## On the existence of Kuiper belt objects bound with Neptune by orbital resonances

### I.A. Gerasimov, B.R. Mushailov

Moscow University Physics Bulletin 1999. 54. N 1. P. 68

Based on a restricted elliptic three-body problem with due account of secular perturbations caused by Uranus, Saturn, and Jupiter, we have evaluated the orbits and regions of stable existence for Transneptune objects that are in orbital commensurability with Neptune.

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Solid state physics

## Effect of water adsorption on the impedance of silicon-porous silicon-metal structures

### S.N. Kozlov, A.N. Nevzorov, A.A. Petrov

Moscow University Physics Bulletin 1999. 54. N 1. P. 82

The effect of water adsorption on the conductivity and the capacity of siliconporous silicon-metal structures has been studied in the frequency range from $10^2$ to $2\cdot10^3$ Hz. It was demonstrated that the sensitivity (as regards the impedance) of the structures studied to the water adsorption effect is maximal in the frequency range from a few hundred Hz to 1 kHz.

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## Interaction between microwaves and semiconductor wafer-mirror structure

### O.G. Koshelev, E.A. Forsh

Moscow University Physics Bulletin 1999. 54. N 1. P. 85

The interference of microwaves in a structure composed of a weakly absorbing wafer, an air gap, and a mirror has been analyzed in a contact less fashion with a view to determining conductivity inhomogeneities in the wafer thickness. It is demonstrated that measuring the reflection coefficient of such a structure at a certain wavelength and an air gap values makes it possible to find the approximate values of the Fourier expansion coefficients of the wafer.

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## Anomalous kinetics of Stabler-Wronski effect in high-resistance $a$-Si:H layers weakly doped with boron

### I.A. Kurova, N.N. Ormont, A.L. Gromadin

Moscow University Physics Bulletin 1999. 54. N 1. P. 89

An anomalous nonmonotonic kinetics of the Stabler-Wronski effect has been discovered for an $a$-Si:H film weakly doped with boron, whose Fermi level was situated near the middle of the forbidden band. Anomalous was the behavior of dark conduction, which was higher than its equilibrium value and exhibited similar nonmonotonic kinetics during and after illumination. The model of formation and relaxation of fast and slow metastable states (broken bonds in silicon and photoactivated boron atoms) was used to show that, after switching off the light, the type of conductivity could change from electronic to hole one, this change being responsible for the anomalous relaxation kinetics.

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