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A. V. Sobolev

Publications and source records attributed to A. V. Sobolev.

10 recordsLinked to original sources
arXiv2026

Stellar Wind of Components of Detached Binary Systems

The paper is devoted to the consideration of the role of the donor stellar wind in the matter exchange between the components of detached binary systems. A classification of close binary systems with interacting components is proposed. A list of potential donors and accretors of such systems, including X-ray binary and symbiotic stars, is given. Analytical tasks have been completed to evaluate the conditions and efficiency of interaction through the stellar wind, a criterion was found for maintaining the self-induced stellar wind of X-ray binaries, and a condition for the formation of an accretion disk during accretion of stellar wind matter by a compact accretor. Three-dimensional gas dynamic models of component interaction are constructed for the five initial velocities of the stellar wind using the example of Sco X-1 type systems. The simulation results are illustrated by pictures of streamlines, temperature distribution, and wind gas densities in the orbital and frontal planes. Model focusing of the donor wind flow by the accretor is confirmed by the observed phase X-ray light curve of Vela X-1.

astro-ph.SR↗
arXiv2018

Modulated magnetic structure of Fe3PO7 as seen by 57Fe Mössbauer spectroscopy

The paper reports new results of the 57Fe Mössbauer measurements on Fe3PO4O3 powder sample recorded at various temperatures including the point of magnetic phase transition TN ~ 163K. The spectra measured above TN consist of quadrupole doublet with high quadrupole splitting of D300K ~ 1.10 mm/s, emphasizing that Fe3+ ions are located in crystal positions with a strong electric field gradient (EFG). In order to predict the sign and orientation of the main components of the EFG tensor we calculated monopole lattice contributions to the EFG. In the temperature range T < TN, the experimental spectra were fitted assuming that the electric hyperfine interactions are modulated when the Fe3+ spin (S) rotates with respect to the EFG axis and emergence of spatial anisotropy of the hyperfine field Hhf = SÃI at 57Fe nuclei. These data were analyzed to estimate the components of the anisotropic hyperfine coupling tensor (Ã). The large anharmonicity parameter, m ~ 0.94, of the spiral spin structure results from easy-axis anisotropy in the plane of the iron spin rotation. The temperature evolution of the hyperfine field Hhf(T) was described by Bean-Rodbell model that takes into account that the exchange magnetic interactions are strong function of the lattice spacing. The obtained Mössbauer data are in qualitative agreement with previous neutron diffraction data for a modulated helical magnetic structure in strongly frustrated Fe3PO4O3.

cond-mat.str-el↗
arXiv2016

On a coefficient in trace formulas for Wiener-Hopf operators

Let $a = a(ξ), ξ\in\mathbb R,$ be a smooth function quickly decreasing at infinity. For the Wiener-Hopf operator $W(a)$ with the symbol $a$, and a smooth function $g:\mathbb C\to~\mathbb C$, H. Widom in 1982 established the following trace formula: \[ {\rm tr}\bigl(g\bigl(W(a)\bigr) - W(g\circ a)\bigr) = \mathcal B(a; g), \] where $\mathcal B(a; g)$ is given explicitly in terms of the functions $a$ and $g$. The paper analyses the coefficient $\mathcal B(a; g)$ for a class of non-smooth functions $g$ assuming that $a$ is real-valued. A representative example of one such function is $g(t) = |t|^γ$ with some $γ\in (0, 1]$.

math.SP↗
arXiv2013

On the spectrum of an "even" periodic Schroedinger operator with a rational magnetic flux

We study the Schrödinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic field is rational. Under these assumptions it is shown that the spectrum of the operator is absolutely continuous. Previously known results on absolute continuity for periodic operators were obtained for the zero magnetic flux.

math.SP↗
arXiv2011

A family of anisotropic integral operators and behaviour of its maximal eigenvalue

We study the family of compact integral operators $\mathbf K_β$ in $L^2(\mathbb R)$ with the kernel K_β(x, y) = \frac{1}π\frac{1}{1 + (x-y)^2 + β^2Θ(x, y)}, depending on the parameter $β>0$, where $Θ(x, y)$ is a symmetric non-negative homogeneous function of degree $γ\ge 1$. The main result is the following asymptotic formula for the maximal eigenvalue $M_β$ of $\mathbf K_β$: M_β= 1 - λ_1 β^{\frac{2}{γ+1}} + o(β^{\frac{2}{γ+1}}), β\to 0, where $λ_1$ is the lowest eigenvalue of the operator $\mathbf A = |d/dx| + Θ(x, x)/2$. A central role in the proof is played by the fact that $\mathbf K_β, β>0,$ is positivity improving. The case $Θ(x, y) = (x^2 + y^2)^2$ has been studied earlier in the literature as a simplified model of high-temperature superconductivity.

math.SP↗
arXiv2009

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

We consider a periodic self-adjoint pseudo-differential operator $H=(-Δ)^m+B$, $m>0$, in $\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in $\bx$, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schrödinger operator with a periodic magnetic potential in all dimensions.

math.SP↗
arXiv2001

Quasi-conformal mappings and periodic spectral problems in dimension two

We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main result is the absolute continuity of the spectra of such operators. The corner stone of the proof is an isothermal change of variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasi-conformal variant of the Riemann mapping theorem.

math.SP↗
arXiv2001

Schrödinger operator on homogeneous metric trees: spectrum in gaps

The paper studies the spectral properties of the Schrödinger operator $A_{gV} = A_0 + gV$ on a homogeneous rooted metric tree, with a decaying real-valued potential $V$ and a coupling constant $g\ge 0$. The spectrum of the free Laplacian $A_0 = -Δ$ has a band-gap structure with a single eigenvalue of infinite multiplicity in the middle of each finite gap. The perturbation $gV$ gives rise to extra eigenvalues in the gaps. These eigenvalues are monotone functions of $g$ if the potential $V$ has a fixed sign. Assuming that the latter condition is satisfied and that $V$ is symmetric, i.e. depends on the distance to the root of the tree, we carry out a detailed asymptotic analysis of the counting function of the discrete eigenvalues in the limit $g\to\infty$. Depending on the sign and decay of $V$, this asymptotics is either of the Weyl type or is completely determined by the behaviour of $V$ at infinity.

math.SP↗