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

## On the quantum Nyquist formula

### B.A. Veklenko$^1$, A.A. Rukhadze$^2$

Moscow University Physics Bulletin 2007. 62. N 4. P. 205

Yu.L. Klimontovich’s assertion on the incorrectness of the quantum Nyquist formula is discussed. It is shown that, in quantum physics, Rytov’s fluctuation formula, the Casimir force theory as treated by E.M. Lifshitz, and the quantum Nyquist formula are all incorrect, as they are united by a common basis.

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## Monte Carlo method for the Schrödinger equation with an asymmetric periodic potential

### D.V. Soldatov

Moscow University Physics Bulletin 2007. 62. N 4. P. 210

A new numerical method is proposed for solving the Cauchy problem for the Schrödinger equation with an asymmetric periodic potential superimposed by a constant electric field. The solution to the Cauchy problem is used to determine the electron’s mean momentum as a function of time, initial conditions, and the applied field. Given an initial state, the mean momentum characterizes the mean current and the conductivity of an asymmetric periodic structure known as the ratchet potential.

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## Numerical simulation of the laminar-turbulent transition in the flow over a backward-facing step

### T.G. Elizarova$^1$, P.N. Nikol’skii$^2$

Moscow University Physics Bulletin 2007. 62. N 4. P. 216

The capabilities of the quasi-gasdynamic equations as applied to the simulation of laminar-turbulent transitions are demonstrated by computing the viscous compressible gas flow in a channel with an abrupt expansion.

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## The mixed finite element method as applied to waveguide diffraction problems

### A.N. Bogolyubov, A.V. Lavrenova

Moscow University Physics Bulletin 2007. 62. N 4. P. 221

A mixed finite element algorithm for solving the vector problem of diffraction by an inhomogeneity in a waveguide is constructed and implemented. Partial radiation conditions are used to proceed to a bounded domain.

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## Some qualitative properties of the Van der Pol equation inferred from its singular set

### I.P. Pavlotsky$^1$, B.I. Sadovnikov$^2$, M. Strianese$^1$

Moscow University Physics Bulletin 2007. 62. N 4. P. 226

It is shown that the singular set of an extended “inverse” integral curve $x(y)$ of the Van der Pol equation is covered with local extrema of $x(y)$ that are stable with respect to small perturbations in the equation. As a consequence, the qualitative behavior of $x(y)$ can be determined and some of its important properties can be understood.

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Solid state physics

## Electron transport in amorphous metal-carbon nanocomposite films

### A.D. Bozhko$^1$, E.A. Kataeva$^2$, T. Takagi$^3$, M.G. Mikheev$^1$, M.B. Guseva$^2$

Moscow University Physics Bulletin 2007. 62. N 4. P. 229

The electrical conductivity of amorphous silicon- and oxygen-containing W-, Nb-, and Cr-carbon nanocomposite films is studied. It is revealed that, at a metal concentration of 10–40 at. % and in the temperature range 80–400 K, the electrical conductivity of the films is a power function of temperature. In terms of inelastic electron tunneling, the average number of localized states in the intercluster potential barriers is calculated as a function of the metal concentration.

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## Dimerization of fluorescent molecular probes on a polystyrene surface

### A.V. Zaitseva$^1$, V.B. Zaitsev$^1$, V.M. Rudoi$^2$

Moscow University Physics Bulletin 2007. 62. N 4. P. 233

Fluorescent spectroscopy is used to demonstrate the effect of vitrification of the surface layer of polystryene on the mobility and dimerization of probe molecules in the layer. The results of this work agree well with the data obtained earlier using an independent technique.

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## X-ray and Mössbauer studies of the Tb$_{0.3}$Dy$_{0.7}$Fe$_{2-x}$Co$_x$ system alloys

### A.S. Ilyushin, S.A. Nikitin, Nguen Van Ngiep, A.A. Opalenko, I.S. Tereshina, A.I. Firov

Moscow University Physics Bulletin 2007. 62. N 4. P. 237

A complex study of the phase composition, atomic and crystalline structure, magnetic properties, and superfine interactions of the Tb$_{0.3}$Dy$_{0.7}$Fe$_{2-x}$Co$_x$ system alloys (${x=0}$-1.3) has been performed. The synthesized alloys are isotypic with the cubic Laves phase (C15 type), their cell parameter monotonically decreases with an increase in the Co content and, hence, the saturation magnetostriction also does. However, the concentration dependences of the Curie temperature, saturation magnetization, and superfine magnetic field strength measured in the Mössbauer experiment display a nonmonotonic (dome-like) character.

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## Calculation of the contribution of conduction electrons to the atomic factors of simple metals

### O.V. Kris’ko, V.M. Silonov, T.V. Skorobogatova, D.A. Kireev

Moscow University Physics Bulletin 2007. 62. N 4. P. 240

An expression for the Fourier transform of the screening electron density of simple metals has been derived using smooth nonlocal model potentials of simple metals. The expression describes the contribution of conduction electrons to the atomic factors of X-ray scattering in simple metals. Aluminum was used as an example for numerical checking. Comparison with the results of similar calculations for the form factor of the Krasko-Gurskii model potential shows the importance of taking the nonlocality of the model potential into account.

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## A consequence from the model description of a decomposing liquid mixture

### L.A. Blagonravov, D.G. Bukin

Moscow University Physics Bulletin 2007. 62. N 4. P. 244

In terms of representation [1] of a decomposing binary liquid mixture as a system of two coupled self-oscillators with partial frequencies $\nu_A$ and $\nu_B$, the following conjecture is verified: given frequency ratios $\nu_A/\nu_B$ and $\nu_A/\nu_C$ for decomposing liquid mixtures $A$-$B$ and $A$-$C$ at the same temperature, it is possible to determine the $\nu_B/\nu_C$ ratio, which is independent of the choice of the A component.

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Geophysics

## Deviation of the Earth’s crust and upper mantle from isostatic equilibrium

### N.A. Chujkova, T.G. Maximova

Moscow University Physics Bulletin 2007. 62. N 4. P. 248

The isostatically unbalanced crust and upper mantle structures conforming to the external gravitational field and minimizing deviation of the internal gravitational field from the isostatic equilibrium field, are determined. A dipole-type distribution of these structures associated with the motion of anomalous masses toward the potential energy minimum is revealed. On the basis of seismic data, it is inferred that the compensation of isostatically unbalanced masses is possible at the core-mantle boundary.

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## General properties of geophysical hydrodynamics models

### K.V. Pokazeev, V.G. Baidulov, M.P. Vasil’ev

Moscow University Physics Bulletin 2007. 62. N 4. P. 255

The influence of simplifying assumptions used in geophysical hydrodynamics models on the general properties of space and time, as well as on the fundamental physical principles that underlie the mechanical systems, is studied. Analysis of the general properties of such models is supplemented by investigation of the peculiarities introduced by stratification into the solutions of nonlinear stationary models. The possibilities for representing the solutions as finite and infinite Fourier series in cylindrical coordinates are explored.

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## Possibilities of radio occultation sounding using the GPS/GLONASS system for regional monitoring of the atmosphere

### V.I. Zakharov, V.E. Kunitsyn

Moscow University Physics Bulletin 2007. 62. N 4. P. 260

The possibilities of retrieving the parameters of atmospheric structures from radio-occultation sounding data are discussed using the examples of a cyclone and an atmospheric front with different parameters. It is shown that the reconstructed images of such structures are highly distorted (up to tens of percents) and often contain artifacts, both factors complicating the interpretation of meteorological data obtained in radio-occultation experiments.

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Atomic and nuclear physics

## Simulations of radio emission from ultrahigh-energy extensive air showers

### N.N. Kalmykov$^1$, A.A. Konstantinov$^1$, R. Engel$^2$

Moscow University Physics Bulletin 2007. 62. N 4. P. 266

The radio emission from extensive air showers with energies up to 1017 eV has been calculated. The calculated lateral distribution of the radio emission is in good agreement with the LOPES-10 experimental data.

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Optics and spectroscopy

## Transversely diffusive edge speckles

### Yu.V. Vasil’ev, A.V. Kozar’, A.E. Luk’yanov

Moscow University Physics Bulletin 2007. 62. N 4. P. 268

A new type of speckles arising upon the diffraction of a laser beam at a sharp metal blade with an imperfect edge is discovered. The phenomenon is explained in terms of the Leontovich gradient mechanism.

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