Faculty of Physics
M.V.Lomonosov Moscow State University
Physics of nuclei and elementary particles

## Symmetries in photonuclear reactions

### B.S. Ishkhanov$^{1,2}$

Moscow University Physics Bulletin 2010. 65. N 2. P. 69

The mechanisms of $\gamma$-quanta interactions with the atomic nuclei and the influence of nucleus asymmetry on the giant dipole resonance structure are discussed.

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Theoretical and mathematical physics

## Electron Weibel instability of plasma with thermal anisotropy

### L.V. Borodachev, D.O. Kolomiets

Moscow University Physics Bulletin 2010. 65. N 2. P. 81

The general pattern of Weibel instability attributed to thermal anisotropic distribution in the electron component is obtained using the technique of discrete simulation of self-consistent radiationless plasma. The dependences of the initial medium anisotropy of the key instability parameters (the characteristic period and the maximum magnetic field energy) are investigated.

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## Investigation of the helicity of magnetic fields on the Sun within the Parker dynamo model

### E.P. Popova, S.N. Nefedov

Moscow University Physics Bulletin 2010. 65. N 2. P. 86

Construction of the butterfly diagrams for the magnetic helicity in several approximations of a Parker dynamo has been carried out. The diagrams are constructed both for the cases of efficient generation of the magnetic field (large dynamo numbers) and for the weak generation (a small dynamo number). The corresponding asymptotic solution to the solar dynamo is used in the first case. The butterfly diagrams for different values of the meridional circulation were studied due to this solution. The butterfly diagrams are constructed and based on the few-mode approximation, which is valid for moderate dynamo numbers. The issue of which butterfly diagram features are common in all these approximations and can be compared with observational data is discussed.

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## Holomorphic extension of the logistic sequence

### D.Yu. Kouznetsov

Moscow University Physics Bulletin 2010. 65. N 2. P. 91

The logistic problem is formulated in terms of the Superfunction and Abelfunction of the quadratic transfer function $H(z)=uz({1-z})$. The Superfunction $F$ as holomorphic solution of equation $H(F(z))=F({z+1})$ generalizes the logistic sequence to the complex values of the argument $z$. The efficient algorithm for the evaluation of function $F$ and its inverse function, id est, the Abelfunction G are suggested;$F\big(G(z)\big)=z$. The halfiteration $h(z)=F({1/2+G(z)})$ is constructed; in wide range of values $z$, the relation ${h(h(z))=H(z)}$ holds. For the special case ${u=4}$, the Superfunction $F$ and the Abelfunction $G$ are expressed in terms of elementary functions.

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## The influence of entropy effects on the adatom diffusion on a cluster surface

### L.S. Bulushova, O.A. Chichigina

Moscow University Physics Bulletin 2010. 65. N 2. P. 99

Slow adatom diffusion on the periodic surface of the upper layer of a growing crystal that has not yet completely formed is considered. Island (cluster) motion is investigated as a factor that accelerates adatom diffusion and results in an entropy increase compared to the case of an already formed stationary substrate layer. The diffusion coefficient, entropy, and the effective temperatures that characterize these properties of the substrate have been introduced.

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## QED effective action in a constant electromagnetic field under conditions of possible Lorentz invariance violation in the Dirac equation

### A.F. Bubnov, V.Ch. Zhukovskii

Moscow University Physics Bulletin 2010. 65. N 2. P. 105

This paper is devoted to the calculation of corrections to QED effective action associated with the axial-vector condensate $b^\mu$, which violate the Lorentz invariance. It was shown that the linear in $b^\mu$ contribution to the 1-loop effective action (Chern-Simons term) is absent in the case of a constant electromagnetic field. The contribution, which is quadratic in $b^\mu$, was calculated for the cases of both constant magnetic and electric fields. Asymptotic estimates of the quadratic in $b^\mu$ term for strong and weak field strengths were obtained.

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Optics and spectroscopy. Laser physics

## A high-intensity bremsstrahlung source for investigating radiation stability of optical samples for excimer laser windows

### A.S. Alimov$^1$, B.S. Ishkhanov$^1$, V.I. Shvedunov$^1$, V.D. Zvorykin$^2$, A.O. Levchenko$^2$, N.N. Ustinovskii$^2$, N.N. Mogilenets$^3$

Moscow University Physics Bulletin 2010. 65. N 2. P. 111

A bremsstrahlung X-ray source ($h\nu\le600$ keV) was developed on the basis of CW electron LINAC. It provides an absorbed dose rate of ∼30 Gy/s within an area of ∼2.5 cm$^2$. The radiation stability of quartz glasses and crystals for excimer lasers windows was investigated.

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Condensed matter physics

## Behavior features of phononless hopping conductivity in the vicinity of the crossover from the linear to quadratic frequency dependence

### M.A. Ormont

Moscow University Physics Bulletin 2010. 65. N 2. P. 115

It was shown that the Coulomb interaction between electrons of “active” (resonance) pairs plays a major role in a wide frequency range. Therefore, the conventional approach to the calculation of the super-linearity of the frequency dependence of ac conductivity, based on the single-particle density of states with a Coulomb gap, is inapplicable to the calculation of high-frequency phononless conductivity. The observed superlinearity of the frequency dependence of the phononless hopping conductivity can manifest itself immediately in the region of the crossover from the linear to quadratic frequency dependence of the conductivity.

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Chemical physics, physical kinetics, and plasma physics

## Diffusion of poly(diallyldimethylammonium chloride) in aqueous solutions with added salt

### A.S. Esakova$^1$, T.V. Laptinskaya$^1$, E.A. Litmanovich$^2$

Moscow University Physics Bulletin 2010. 65. N 2. P. 119

The peculiarities of the fluctuation motions of diallyldimethylammonium chloride polyions (PDADMAC) in 0.01M, 0.025M, and 0.05M NaCl aqueous solutions were studied depending on the polyion concentration by means of dynamic and static light scattering. The behavior of the system in a transitional region between dilute and unentangled semidilute solutions was investigated. The nature of the fastest and slowest motion modes is discussed; additional modes observed upon scattering in semidilute solutions were attributed to interaction modes.

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Astronomy, astrophysics, and cosmology

## Some properties of discontinuous flows near magnetic reconnection regions

### L.S. Ledentsov$^1$, B.V. Somov$^2$

Moscow University Physics Bulletin 2010. 65. N 2. P. 126

The graphic presentation of the dependence between the angles of the magnetic field relative to the discontinuity surface normal at both of its sides is found within the frame of the classical formulation of the problem of discontinuous magnetohydrodynamic (MHD) flows. The result is applied to the known class of analytical solutions concerning the structure of a magnetic field in the vicinity of a reconnecting current layer.

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Physics of Earth, atmosphere, and hydrosphere

## The system of currents above a complex bottom relief and its influence on the transfer of admixtures

### B.I. Samolyubov$^1$, T.V. Kirillova$^2$

Moscow University Physics Bulletin 2010. 65. N 2. P. 132

This article describes the results of natural and theoretical investigations of the fields of the current velocity and water composition parameters in a system of stratified currents above a complex bottom relief. Current velocity distributions were obtained and verified, taking into account all the flows included in the system. The dependencies of the distributions of the concentrations of diluted oxygen and chlorophyll-a upon the parameters of jet and near-bottom density currents were revealed.

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## Density inhomogeneities of the Earth’s mantle and core

### N.A. Chuikova, T.G. Maksimova

Moscow University Physics Bulletin 2010. 65. N 2. P. 137

Lateral density variations are determined at depth and are characterized by the anomalies of the seismic waves velocities, which are consistent with both the anomalies of the external gravity field and with the data from the analysis of Earth’s free-oscillation minimizing the deviations of the internal Earth structure from a hydrostatically equilibrated structure. It is shown that the obtained anomalous structures cause anomalies of the gravity field inside the Earth, which may be conducive to convective movements in the mantle and core.

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Theoretical and mathematical physics

## Conditional density matrix: Entangled states in the Heisenberg representation

### O.D. Timofeevskaya

Moscow University Physics Bulletin 2010. 65. N 2. P. 145

The application of the conditional density matrix in the Heisenberg representation to the processes caused by entanglement allows elimination of any misunderstanding of these phenomena. We consider quantum entanglement of two- and four-particle systems, quantum correlations different from entanglement, and their causes.

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Astronomy, astrophysics, and cosmology

## Spatiotemporal structure of pulses in detectors of Cherenkov light of extensive atmospheric showers

### D.A. Podgrudkov$^1$, L.G. Dedenko$^1$, T.M. Roganova$^2$, G.F. Fedorova$^2$

Moscow University Physics Bulletin 2010. 65. N 2. P. 152

We calculated the pulses of the Cherenkov light of extensive atmospheric showers in Cherenkov radiation detectors at the Yakutsk array in the framework of the QGSJET-II model. It is shown that the calculated width of a pulse of Cherenkov light in a vertical proton-induced shower of energy of $10^{18}$-$10^{20}$ eV increases from 50 ns at a distance of 200 m from the shower axis to 700 ns at a distance of 1 km.

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## Magnetic field correlation tensor in spaces of constant curvature

### A.S. Rubashnyi$^1$, D.D. Sokoloff$^2$

Moscow University Physics Bulletin 2010. N 2.

The concept of statistical homogeneity and isotropy for vector fields in spatial sections of constant curvature was analyzed. Solenoidality conditions for a corresponding correlation tensor were obtained for positive and negative curvature. It was shown that these conditions differ from the corresponding condition for fields in Euclidean space.

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