The results of RHEED, FTIR and Raman spectroscopy study of silicon and germanium films with the thickness up to 200 nm grown from molecular beams on dielectric Si$_3$N$_4$/SiO$_2$/Si(001) substrates are presented. Noticeable changes of the intensity of the N$-$H and Si$-$N absorption bands have been observed in the IR absorbance spectra as a result of the deposition of the silicon and germanium films. The thicker was the deposited film, the more considerable were the decrease of N$-$H absorption band intensity and the increase in that of the Si$-$N band. This tendency has been observed during the growth of both amorphous and polycrystalline Si or Ge films. The reduction of IR absorption at the band assigned to the N$-$H bond vibration is explained by breaking of these bonds followed by the diffusion of the hydrogen atoms from the Si$_3$N$_4$ layer into the growing film of silicon or germanium. The effect of the deposited film thickness on the diffusion of hydrogen is discussed within a model of the diffusion of hydrogen atoms controlled by the difference in chemical potentials of hydrogen atoms in the dielectric Si$_3$N$_4$ layer and the growing silicon or germanium film. Hydrogen atoms escape from the Si$_3$N$_4$ layer only during the deposition of a Si or Ge film when its thickness gradually grows. The interruption of the film growth stops the migration of hydrogen atoms into the film because of the decline in the chemical potential difference.

Larisa V. Arapkina Kirill V. Chizh Dmitry B. Stavrovskii Alexey A. Klimenko Alexander A. Dudin Vladimir P. Dubkov Mikhail S. Storozhevykh Vladimir A. Yuryev

Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\le p<\infty$, and pointwise convergence for functions in $L^\infty$. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.

Alexander Bufetov Mikhail Khristoforov Alexey Klimenko

The problem of 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with retarded and advanced interactions is investigated.

Stanislav V. Klimenko Igor N. Nikitin Wasil F. Urazmetov

We study how small perturbations of a 2-by-2 complex matrix can change its canonical form for *congruence. We construct the Hasse diagram for the closure ordering on the set of *congruence classes of 2-by-2 matrices.

Vyacheslav Futorny Lena Klimenko Vladimir V. Sergeichuk

We study the competition of quark-antiquark and diquark condensates under the influence of an external chromomagnetic field modelling the gluon condensate and in dependence on the chemical potential and temperature. As our results indicate, an external chromomagnetic field might produce remarkable qualitative changes in the picture of the color superconducting (CSC) phase formation. This concerns, in particular, the possibility of a transition to the CSC phase and diquark condensation at finite temperature.

D. Ebert V. V. Khudyakov K. G. Klimenko V. Ch. Zhukovsky

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.

D. Ebert K. G. Klimenko A. V. Tyukov V. Ch. Zhukovsky

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential $\mu_I$. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation phase is realized for arbitrary small nonzero $\mu_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $\nu\sim\mu_I$ and $\lambda\sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(\lambda,\nu)$ there is a strip $0\le\lambda<\lambda_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).

D. Ebert K. G. Klimenko A. V. Tyukov V. Ch. Zhukovsky

The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one.

N. V. Gubina K. G. Klimenko S. G. Kurbanov V. Ch. Zhukovsky

In this note we give the answer to the question posed by V. N. Dubinin concerning covering properties of complex polynomials

Alexey Solyanik

The influence of an external constant and homogeneous magnetic field H on the phase structure of the P-symmetric, chiral invariant 3-dimensional field theory model with two four-fermion interaction structures is considered. An arbitrary small (nonzero) magnetic field is shown to induce spontaneous violation of the initial symmetry (magnetic catalysis). Moreover, vacuum of the model at H>0 can be either P-symmetric or chiral invariant, depending on the values of the coupling constants.

V. Ch. Zhukovsky K. G. Klimenko V. V. Khudyakov